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Abraham Berman

May 2013
Linear Algebra and its Applications 438(10)

DOI:10.1016/j.laa.2012.11.001

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Wayne Barrett

Wayne Barrett

Naomi Shaked-Monderer

Max Stern Academic College of Emek Yezreel

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Linear Algebra and its Applications 438 (2013) 3724–3734

Contents lists available at SciVerse ScienceDirect

Linear Algebra and its Applications

journal homepage: www.elsevier.com/locate/laa

Abraham Berman

Avi (Abraham) Berman was born in Haifa in 1943. He received his B.Sc. (1966) and M.Sc. (1968) in

mathematics from the Technion.In 1970 he received his Ph.D. in applied mathematics from Northwest-

ern University. After 2 years in Montreal, Canada, he returned to Israel.The Department of Mathematics

at the Technion became his professional home, from the beginning as a Senior Lecturer in 1972 until his

retirement in 2011 as a Professor and holder of the Israel Pollack Academic Chair, and continuing now

as Professor Emeritus. Since 1995 he also held a parallel position of a Professor in the Department of

Education in Sciences and Technology at the Technion. In the years 1990–1997 he served as head of the

Center of Pre-University Studies, and in the years 2007–2010 as head of the Department of Education

in Sciences and Technology, both at the Technion. Between 2007 and 2010 he was also Head of the

Israeli Society for Promotion of and Research on Creativity and Giftedness.

While Avi’s permanent professional home is the Technion, he enjoyed many long and short visits

to universities in ﬁve continents. In particular he is a frequent visitor to the Hamilton Institute at

the National University of Ireland, Maynooth, where he serves as one of the scientiﬁc advisors of the

institute.

Avi was co-organizer of 16 Haifa Matrix Theory conferences – the ﬁrst one in 1984, and the sixteenth

to be held in the end of 2012. In his role as advisor to the Hamilton Institute he co-organized several

Hamilton Workshops on Nonnegative Matrices and Related Topics.

Avi’s main areas of interest in mathematics is Matrices, Graphs and the connections between the

two. His list of publications includes papers on linear inequalities over cones, stability, proper splitings,

http://dx.doi.org/10.1016/j.laa.2012.11.001

Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734 3725

completely positive matrices, transmission control protocol (TCP), sign patterns, minimum rank, and

graph spectra (the Colin de Verdière parameter).

Avi’s best known publication is probably the often-cited, and by now classical, book Nonnegative

Matrices in the Mathematical Sciences, co-authored with Robert Plemmons. The ﬁrst edition published

in 1979 by Academic Press, and the second revised edition in 1994 by SIAM, in its Classics in Applied

Mathematics series. He is the author or co-author of several other books: Cones, Matrices and Mathe-

matical Programming (1973), Nonnegative Matrices in Dynamic Systems (1989, co-authors M. Neumann

and R.J. Stern), and Compeltely Positive Matrices (2003, co-author N. Shaked-Monderer), and a Hebrew

textbook Linear Algebra (1999, co-author B.Z. Kon).

Avi’s passion for mathematics in general and linear algebra in particular is accompanied by a keen

interest in mathematics eduction. He published papers in the area of Creativity and Giftedness, and in

the area of University Teaching (especially, teaching linear algebra).

Avi supervised 19 Ph.D. students and 14 M.Sc. students, and is currently supervising ﬁve more Ph.D.

students and two more M.Sc. students. Those who were lucky to be his students gained a mentor, a

friend, and a source of support that does not end with the completion of the degree.

Avi’s devotion to mathematics and education, and his loyalty to his friends, is surpassed only by his

devotion to his family: his wife Dalia, his three daughters and his 10 grandchildren.

List of Publications (Abraham Berman)

Theses:

M.Sc. Thesis: A. Berman, The permanent and other generalized matrix functions,

Technion, 1968.

Ph.D. Thesis: A. Berman, Linear inequalities in matrix theory, Northwestern, 1970.

In Print

1. A. Berman and A. Ben-Israel, More on linear inequalities with applications to matrix theory, J.

Math. Anal. Appl., 33 (1971), 482–496.

2. A. Berman and A. Ben-Israel, A note on pencils of Hermitian or symmetric matrices, SIAM J. Appl.

Math., 21 (1971), 41–54.

3. A. Berman and A. Ben-Israel, Linear inequalities, mathematical programming and matrix theory,

Math. Programming, 1 (1971), 291–300.

4. A. Berman and P. Gaiha, A generalization of irreducible monotonicity, Linear Algebra and its

Appl., 5 (1972), 29–38.

5. A. Berman and R.J. Plemmons, Monotonicity and the generalized inverse, SIAM J. Appl. Math.,

22 (1972), 155–161.

6. A. Berman, Consistency of linear ineqalities over sets, Proc. Amer. Math. Soc., 36 (1972), 13–17.

7. A. Berman and A. Ben-Israel, Linear equations over cones with interior; a solvability theory with

applications to matrix theory, Linear Algebra and its Appl., 7 (1973), 139–149.

8. A. Berman, Linear inequalities over complex cones, Canad. Math. Bull., 16 (1973), 19–21.

9. A. Berman, Complementary problem and duality over convex cones, Canad. Math. Bull., 7 (1974),

19–25.

10. A. Berman and R.J. Plemmons, Cones and iterative methods for best least squares solutions to

linear systems, SIAM J. Numer. Anal., 1 (1974), 145–154.

11. A. Berman and R.J. Plemmons, Inverses of nonnegative matrices, Linear and Multilinear Algebra,

2 (1974), 161–172.

12. A. Berman and R.J. Plemmons, Matrix group monotonicity, Proc. Amer. Math. Soc., 46 (1974),

355–359.

13. A. Berman, Nonnegative matrices which are equal to their generalized inverses, Linear Algebra

and its Appl., 9 (1974), 261–265.

3726 Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734

14. A. Berman and R.J. Plemmons, Eight types of matrix monotonicity, Linear Algebra and its Appl.,

13 (1976), 115–123.

15. A. Berman and M. Neumann, Proper splittings of rectangular matrices, SIAM J. Appl. Math., 31

(1976), 307–312.

16. A. Berman with M. Neumann, Consistency and splittings, SIAM J. Numer. Anal., 13 (1976), 877–

888.

17. A. Berman and R.C. Ward, Stability and semipositivity of real matrices, Bull. Amer. Math. Soc.,

83 (1977), 262–263.

18. A. Berman and A. Kotzig, The length of a (0,1) matrix, Linear Algebra and Appl., 20 (1978), 197–

203.

19. G.P. Barker, A. Berman and R.J. Plemmons, Positive diagonal solutions to the Lyapunov equation,

Linear and Multilinear Algebra, 5 (1978), 249–256.

20. A. Berman and M. Tarsi, On Tucker’s key theorem, Internal J. Math. Sciences, 1 (1978), 63–68.

21. A. Berman, The spectral radius of a nonnegative matrix, Canad. Math. Bull., 2 (1978), 113–114.

22. A. Berman and R.C. Ward, ALPS: Classes of stable and semi-positive matrices, Linear Algebra and

Appl., 21 (1978), 163–174.

23. A . Berman, R.S. Vargaand R.C. Ward, ALPS: Matrices with nonpositive off-diagonal entries, Linear

Algebra and Appl., 21 (1978), 233–244.

24. A. Berman and A. Kotzig, The order of cyclicity of bipartite tournaments and (0,1) matrices,

Kyungpook Math. J., 19 (1978), 127–134.

25. A. Berman, Generalized interval programming, Bull. Calcutta Math. Soc., 71 (1980), 169–176.

26. A. Berman and A. Kotzig, Bipartite graphs with a central symmetry and (0,1) matrices, Annals of

Discrete Math., 8 (1980), 37–42.

27. A. Berman, B.N. Parlett and R.J. Plemmons, Diagonal scaling to an orthogonal matrix, SIAM J. on

Algebraic and Discrete Methods, 2 (1981), 57–65.

28. A. Berman and B.D. Saunders, Matrices with zero line sums and maximal rank, Linear Algebra

and its Appl., 40 (1981), 229–235.

29. A. Berman, Matrices and the linear complementarity problem, Letters in Linear Algebra, 40

(1981), 249–256.

30. A. Berman, Skew Hadamard matrices of order 16, Annals of Discrete Math., 12 (1982), 45–47.

31. R. Aharoni, A. Berman and Y. Censor, An interior points algorithm for the convex feasibility

problem, Advances in Applied Mathematics, 4 (1983), 479–489.

32. D. Hershkowitz and A. Berman, Necessary conditions and a sufﬁcient condition for the Fischer-

Hadamard inequalities, Linear and Multilinear Algebra, 13 (1983), 67–72.

33. A. Berman and D. Hershkowitz, Matrix diagonal stability and its implications, SIAM J. on Algebraic

and Discrete Methods, 4 (1983), 377–382.

34. D. Hershkowitz and A. Berman, Localization of the spectra of P- and P0-matrices, Linear Algebra

and Appl., 52/53 (1983), 387–397.

35. A. Berman, Convexity, graph theory and nonnegative matrices, Annals of Discrete Math., 20

(1984), 55–59.

36. A. Berman and D. Hershkowitz, Characterization of acyclic D-stable matrices, Linear Algebra and

Appl., 58 (1984), 17–31.

37. D. Hershkowitz and A. Berman, Notes on w- and t-matrices, Linear Algebra and Appl., 58 (1984),

169–183.

38. A. Berman, D. Hershkowitz and C.R. Johnson, Linear transformations that preserve certain pos-

itivity classes of matrices, Linear Algebra and Appl., 68 (1985), 9–29.

39. O. Kessler and A. Berman, Matrices with a transitive graph and inverse M-matrices, Linear Algebra

and its Appl., 71 (1985), 175–185.

40. A. Berman and D. Hershkowitz, Graph theoretical methods in studying stability, Contemporary

Math., 47 (1985), 1–6.

41. A. Berman, M. Neumann and R.J. Stern, Cone reachability for non-diagonal linear differential

systems, Linear Algebra and its Appl. (1986), 263–280.

Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734 3727

42. D. Shasha and A. Berman, On the uniqueness of the Lyapunov scaling factors, Linear Algebra and

its Appl., 91 (1987), 53–63.

43. A. Berman and D. Hershkowitz, Combinatorial results on completely positive matrices, Linear

Algebra and its Appl., 95 (1987), 111–125.

44. A. Berman and R.J. Stern, Linear feedback, irreducibility and M-matrices, Linear Algebra and its

Appl., 97 (1987), 141–152.

45. A. Berman and B. Grone, Bipartite completely positive matrices, Proc. of the Cambridge Phil.

Society, 103 (1988), 269–276.

46. A. Berman and A. Kotzig, Cross cloning and antipodal graphs, Discrete Mathematics, 69 (1988),

107–114.

47. A. Berman, Complete positivity, Linear Algebra and its Applications, 107 (1988), 57–63.

48. A. Berman and S.K. Jain, Nonnegative generalized inverses of powers of nonnegative matrices,

Linear Algebra and its Applications, 10 (1988), 169–179.

49. D. Shasha and A. Berman, More on the uniqueness of the Lyapunov scaling factors, Linear Algebra

and its Applications, 107 (1988), 253–273.

50. A. Berman and D. Shasha, Inertia preserving matrices, SIAM Journal on Matrix Analysis and

Applications, (1991), 209–219.

51. N. Shaked-Monderer and A. Berman, More on extremal positive semideﬁnite doubly stochastic

matrices, Linear Algebra and its Applications, 167 (1992), 17–34.

52. N. Kogan and A. Berman, Characterization of completely positive graphs, Discrete Mathematics,

114 (1993), 297–304.

53. A. Berman and D. Shasha, Strongly inertia preserving matrices SIAM Journal on Matrix Analysis

and Applications, 15 (1994), 729–732.

54. R. Leikin, A. Berman and O. Zaslavsky, The role of symmetry in mathematical problem solving:

an interdisciplinary approach, Symmetry: Culture and Science, 6 (1995), 332–335.

55. A. Berman and D. Shasha, Set inertia preserving matrices, Set inertia preserving matrices, Linear

and Multilinear Algebra, 43 (1997), 169–179.

56. A. Berman and M. Krupnik, Spectrum preserving lower triangular case, Electronic J. Linear Al-

gebra, 2 (1997), 9–16.

57. A. Berman and R. J. Plemmons, A note on simultaneous diagonalizable matrices, Mathematical

Inequalities and Applications 1 (1998), 149–152.

58. A. Berman and N. Shaked-Monderer, Remarks on completely positive matrices, Linear and Mul-

tilinear Algebra, 44 (1998), 149–163.

59. R. Leikin, A. Berman and O. Zaslavsky, On the deﬁnition of symmetry, Symmetry: Culture and

Science, 9 (1998), 375–382.

60. A. Berman and X. D. Zhang, A note on degree antiregular graphs, Linear and Multilinear Algebra,

47 (2000), 307–311.

61. A. Berman and X. D. Zhang, Lower bounds for the eigenvalues of Laplacian matrices, Linear

Algebra and its Applications, 316 (2000), 13–20.

62. M. Berezina and A. Berman, ‘Proof reading’ and multiple choice tests, International Journal of

Mathematical Education in Science and Technology, 31 (2000), 613–619.

63. R. Leikin, A . Berman and O. Zaslavsky, Applications of symmetry to problemsolving, International

Journal of Mathematical Education in Science and Technology 31 (2000), 799–809.

64. R. Leikin, A. Berman and O. Zaslavsky, Learning through teaching: The case of symmetry, Math-

ematics Education Research Journal, 12 (2000), 16–34.

65. A. Berman and X. D. Zhang, On the spectral radius of graphs with cut vertices, Journal of Com-

binatorial Theory, Series B 83 (2001), 233–240.

66. B. Abramovitz, M. Berezina and A. Berman, Incorrect but instructive, International Journal of

Mathematical Education in Science and Technology, 33 (2002), 465–475.

67. A. Berman and S. Gueron, A note on the inverse of Hilbert matrix, The Mathematical Gazette, 86

(2002), 274–277.

68. F. Barioli and A. Berman, The maximal cp-rank of rank kcompletely positive matrices, Linear

Algebra and its Applications, 363 (2003), 57–63.

3728 Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734

69. A. Berman and X. D. Zhang, Bipartite density of cubic line graphs, Discrete Math., 260 (2003),

27–35.

70. A. Berman, Graphs of matrices and matrices of graphs, Numerical Mathematics, a Journal of Chinese

Universities (English series) Vol. 12 (supplement) (2003), 12–14.

71. B. Abramovitz, M. Berezina and A. Berman, Useful mistakes, International Journal of Mathemat-

ical Education in Science and Technology.

72. B. Koichu and A. Berman, 3-D dynamic geometry: Ceva’s Theorem in space, International Journal

of Computers for Mathematical Learning, 9 (2004), 95–108.

73. B. Koichu, A. Berman and M. Moore, Promoting heuristic literacy, For the Learning of Mathemat-

ics, 24 (1) (2004), 33–39.

74. A. Berman, R. Shorten and D. Leith, Positive matrices associated with synchronized communi-

cation networks, Linear Algebra and its Applications, 393 (2004), 47–54.

75. A . Berman and C. Xu, 5 ×5 completely positive matrices, Linear Algebra Appl., 393 (2004), 55–71.

76. B. Abramovitz, M. Berezina and A. Berman, How not to formulate multiple choice problems, Int.

J, Math. Ed. Sci. Technol., 36(4) (2005).

77. A. Berman and K. H. Foerster, Algebraic connectivity of trees with a pendant edge of inﬁnite

weight, Electronic J. Linear Algebra, 13 (2005), 175–186.

78. A . Berman and C. Xu, [0,1]completely positive matrices, Linear Algebra Appl., 399 (2005), 35–51.

79. A. Berman and T. Laffey, Similarity classes and principal submatrices, Linear Algebra Appl., 401

(2005), 341–351.

80. B. Koichu and A. Berman, When do gifted high-school students use geometry to solve geometry

problems? Journal of Secondary Gifted Education, XVI (2005), 168–179.

81. A. Berman, F. Goldberg and B. Koichu, ‘Good research’ conducted by talented high school stu-

dents: The case of SciTech, Gifted Education International, 20 (2005), 220–228.

82. A. Berman, T. Laffey, A. Leizarowitz and R. Shorten, On the second eigenvalue of matrices asso-

ciated with TCP, Linear Algebra Appl., 416 (2006), 175–183.

83. A. Berman and U. G. Rothblum, A note on the computation of the CP-rank, Linear Algebra Appl.,

419 (2006), 1–7.

84. B. Koichu, A. Berman, and M. Moore, Heuristic literacy development and its relation to mathemat-

ical achievements of middle school students, Instructional Science (Published online) (2006).

85. B. Koichu, A. Berman, and M. Moore, The effect of promoting heuristic literacy on the mathematic

aptitude of middle-school students, International Journal of Mathematical Education in Science

and Technology, 38 (2007), 1–17.

86. A. Berman and C. Xu, Minimal (0,1) cp matrices, Linear and Multilinear Algebra, 5 (2007), 439–

456.

87. I. Verner, A. Aroshas, and A. Berman, An experiment on integrating supplementary application-

based tutorials in the multivariable calculus course, International Journal of Mathematical Ed-

ucation in Science and Technology, 39 (2008), 427–442.

88. B. Koichu, A. Berman, and M. Moore, The effect of promoting heuristic literacy on the mathematic

aptitude of middle-school students, International Journal of Mathematical Education in Science

and Technology, 38 (2007), 1–17.

89. A .Berman, S. Friedland, L.Hogben, U.G.Rothblum and B.Shader, An upper bound for the minimum

rank of a graph, Linear Algebra Appl., 429 (2008), 1629–1638.

90. A.Berman, S. Friedland, L.Hogben, U.G.Rothblum and B.Shader, Minimum rank of matrices de-

scribed by a graph or pattern over the rational, real and complex numbers, Electronic Journal of

Combinatorics, 15/1 (2008).

91. B. Abramovitz, M. Berezina, A. Berman and L. Shvartsman, How to understand a theorem, Inter-

national Journal of Mathematical Education in Science and Technology, 40,5 (2009), 577–588.

92. A. Berman, M. Catral, L. Dealba, A. Elhashasha, F. Hall, L. Hogben, I. Kim, S. Olesky, P. Tarazaga,

M. Tsatsomeros and P. Van den Driessche, Sign Patterns that allow eventual positivity, Electronic

J. Linear Algebra, 17 (2010), 108–120.

93. A. Agnis, A. Berman and B. Koichu, Intercultural aspects of creativity, Mediterranean Journal for

Research in Mathematical Education, 9 (2010), 107–117.

Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734 3729

94. A. Berman, The history of Linear Algebra in Israel – a personal view , IMAGE 44 (2010), 22–24.

95. F. Goldberg and A. Berman, On the Colin de Verdiere number of Graphs, Linear Algebra Appl.,

(2011).

96. A. Berman and D. Shasha , Completely Positive House Matrices, Linear Algebra Appl., 436 (2012),

12–26.

97. M. Farber and A. Berman, A lower bound for the second largest Laplacian eigenvalueof a weighted

graph, Electronic Journal of Linear Algebra.

98. I. Kontorovich B. Koichu, R. Leikin and A. Berman, A framework for handling the complexity of

students mathematics problem posing in small groups, Journal of Mathematical Behavior, 31

(2012), 149–161.

99. A. Berman, C. King and R. Shorten, Common diagonal stability and co-stability, Linear and Mul-

tilinear Algebra (Accepted).

100. A. Shlote, F. Wirth, A.Berman and R. Shorten, on the higher moments of TCP, Linear Algebra and

its Applications (Accepted).

Conference Proceedings

1. A. Berman, Incidence matrices of Boolean functions and (0,1)programming, in: “Applications

of Number Theory to Numerical Analysis”, edited by S.K. Zaremba, Academic Press, New York–

London, 1972., 465–477.

2. A. Berman, A. Evyatar and T. Globerzon, Mathematical patterns for gifted children, in: “Gifted

Children: Challenging their Potential, New Perspectives and Alternatives”, edited by A. Evyatar,

Trillium Press, N.Y., 1981, pp. 71–81.

3. A. Berman, Stable acyclic matrices, Proceedings of the Conference on Linear Algebra and its

Applications, Vitoria, Spain, 1983.

4. M.A. Pollatschek, A. Berman, Z. Rosberg and A. Zaks, The gain of common inventory, Proceedings

of the Industrial Engineering/Management Science Conference, Tel-Aviv, 1984.

5. A. Berman, A. Kotzig and G. Sabbidussi, Antipodal graphs of diameter 4 and extremal girth, Con-

temporary Methods, in: “Graph Theory”, edited by R. Bodendiek,

Wissenschaftsverlag, Manheim/Wien/Zurich, 1990, pp.137–150.

6. A. Berman, mapplications of M-matrices, in: “Systems and Management Science by Extremal

Methods”, edited by F. Y. Phillips and J. J. Rousseau, Kluwer Academic Publishers, Boston, Dor-

drecht, London, 1992, pp. 15–126.

7. A. Berman, Completely positive graphs, in: “Combinational and Graph Theoretical Problems in

Linear Algebra”, edited by R. Brualdi, S. Friedland and V. Klee, Springer, NY, 1993, pp. 229–233.

8. R. Leikin, A. Berman and O. Zaslavsky, Deﬁning and understanding symmetry, in: “Proceedings

of the 21st International Conference for the Psychology of Mathematical Education”, edited by

J. P. da Ponte and J. F. Matos, Vol. 3, 1997, pp. 192–199.

9. B. Koichu and A. Berman, “The research work of talented high school students at the Technion”,

Creativity in Mathematics, Riga, Latvia, 2002.

10. B. Koichu, A. Berman and M. Moore, Changing teachers’ beliefs about student’ heuristics in

problem solving, CERME, 3, 2003.

11. S. Aroshas and A. Berman, Mathematical problems used to identify gifted students, in: “Pro-

ceedings of the 3rd international Conference on Creativity in Mathematics Education and the

Education of Gifted Students”, edited by E. Velikova, 2003, pp. 310–313. Rousse, Bulgaria, Uni-

versity of Rousse.

12. B. Koichu, A. Berman, M. Moore, Very able students think aloud: An attempt at heuristic mi-

croanalysis, in:“Proceedings of the 3rd international Conference on Creativity in Mathematics

Education and the Education of Gifted Students”, edited by E. Velikova, 2003, pp. 318–325.

Rousse, Bulgaria, University of Rousse.

13. A. Berman, R. Shorten and D. Leith, Convergence results for synchronised communication net-

works, 2004 American Control Conference.

3730 Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734

14. A. Berman and F. Goldberg, Mathematical researchexperience of talented high school students in

Sci-Tech, in: “Proceedings of the 4th Mediterranean Conference on Research in Math Education”,

edited by A. Gagatsis, 2005, pp. 561–570.

15. S. Aroshas, I. Verner and A. Berman, Calculus for engineers: an applications motivated approach,

in: “Proceedings of the 4th Mediterranean Conference on Research in Math Education”, edited

by A. Gagatsis, 2005, pp. 591–598.

16. B. Abramovitz, M. Berezina, A. Berman and L. Shvarsman, “Procedural” is not enough, in: “Pro-

ceedings of the 4th Mediterranean Conference on Research in Math Education”, edited by

A. Gagatsis, 2005, pp. 599–608.

17. A. Berman, A. Malek, K. Shir and J. Thimor, Teachers specialization – an intermediate report, in:

“Proceedings of the 4th Mediterranean Conference on Research in Math Education”, edited by

A. Gagatsis, 2005, pp. 673–678.

18. S. Aroshas, I. Verner, and A. Berman, Integrating Applications in the Technion Calculus Course:

A Supplementary Instruction Experience. American Society of Engineering Education Annual

Conference, Chicago, Illinois, 2006.

19. B. Koichu, A. Berman and M. Moore, Patterns of middle school students’ heuristic behaviors in

solving seemingly familiar problems. In J. Novotna, H. Moraova, M. Kratka, and N. Stehlikova

(Eds.), Proceedings of the 30th Conference of the International Group for the psychology of

Mathematics Education, 3, 457–464, Prague, Czech Republic: Charles University, 2006.

20. A . Berman, Nonnegative Matrices – Old Problems and New Results, pp. 1-9 in C.Commault and N.

Marchands (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, Springer,

Berlin-Heidelberg, 2006.

21. S. Aroshas, I. Verner, and A. Berman, The Effect of Integrating Applications in the Technion

Calculus Course. Mathematical Modelling (ICTMA 12): Education, Engineering and Economics

(C. Haines et al., Eds.), in press.

22. B. Abramovitz, M. Berezina, A. Berman and L. Shvartsman, What does the theorem mean? In:

CERME 5, 2007.

23. A. Berman, I. Verner and S. Aroshas, The Teaching Calculus with Applications Experiment

succeeded–Why and What Else? In: CERME 5, 2007.

24. B. Koichu, E. Katz and A. Berman, What is a beautiful problem? An undergraduate students’

perspective, Proceedings of the 31st Conference of the International Group for the Psychology

of Mathematics Education, Seoul, Korea, 2007.

Special Issues (editor)

1. A. Berman, Y. Censor and H. Schneider, Haifa 1985 Conference on Matrix Theory, Lin. Alg. and

Appl., 80 (1986), 173–260.

2. A. Berman, D. Hershkowitz and L. Lerer, Haifa 1988 Conference on Matrix Theory, Lin. Alg. and

Appl., 120 (1989), 237–269.

3. A. Berman, L. Elsner, M. Goldberg and R. Loewy, The ninth ILAS conference, Lin. Alg. and Appl.,

361 (2003), 1.

4. A. Berman and T. Laffey, Preface, Electronic J. Linear Algebra, 12 (2004–2005), 1.

5. A. Berman, L. Lerer and R. Loewy, Haifa 2005 Conference on Matrix Theory, Lin. Alg. and Appl.,

416 (2006) .

6. A. Berman, C. Krattenthaler, S. M. Rump, I. Spitkovsky and F. Zhang, Preface, Lin. Alg. and Appl.

Special Issue in Honor of S. Friedland (2009).

7. R. Leikin and A. Berman, Mediterranean Journal for Research in Mathematics Education, Special

Issue on Intercultural Aspects of Creativity (2010).

Books

1. A. Berman, Cones, Matrices and Mathematical Programming, Lecture Notes in Economic and

Mathematical Systems 79, Springer Verlag, Berlin– Heidelberg–New York, 1973.

Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734 3731

2. A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Computer

Science and Applied Mathematics, Academic Press, 1979.

3. A. Berman, M. Neumann and R.J. Stern, Nonnegative Matrices in Dynamic Systems, Pure and

Applied Mathematics, Wiley, 1989.

4. A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, (Revision of

[2]), Classics in Applied Mathematics, SIAM, Philadelphia, 1994.

5. A. Berman and B. Z. Kon, Linear Algebra (in Hebrew), BAK, Haifa, 1999.

6. A. Berman and N. Shaked-Monderer, Completely Positive Matrices, World Scientiﬁc, 2003.

Books (editor)

1. A. Berman, School Mathematics 2000 (in Hebrew), The S. Neeman Foundation, Haifa, 1989.

2. A. Berman, Promoting Excellence in Science and Technology Education (in Hebrew), The S. Nee-

man Foundation, Haifa, 1990.

3. A. Berman and S. Gueron, Promoting Mathematical Talents (in Hebrew), The S. Neeman Foun-

dation, Haifa, 2002.

4. R. Leikin, A. Berman and B. Koichu, Creativity in Mathematics and the Education of Gifted Stu-

dents, Sense Publishers, 2009.

Chapters in Books

1. A. Berman and N. Shaked-Monderer, Nonnegative matrices and digraphs, in: R.A. Meyers (Ed.),

Encyclopedia of Complexity and System Sciences, Springer, 2009.

2. A. Berman and G. Leder, The pleasure of teaching the gifted and the honor of learning from them,

pp. 3-10, in: R. Leikin, A. Berman and B. Koichu (Eds.), Creativity in mathematics and the education

of gifted students, Sense Publishers, 2009.

3. R. Leikin, B. Koichu and A. Berman, Mathematics giftedness as a quality of problem solving acts,

pp. 115–127, in: R. Leikin, A. Berman and B. Koichu (Eds.), Creativity in mathematics and the

education of gifted students, Sense Publishers, 2009.

4. B. Amit, M. Movshovity-Hadar and A. Berman, Exposure to mathematics in the making, Recent

Developments on Introducing a Historical Dimensions in Mathematical Education, V. Katz and

C. Tzanakis, editors, (2012).

Book Reviews

1. A. Berman, Book review on “Generalized inverses of linear transformations” by S.L. Campbell

and C.D. Meyer, SIAM Rev., 23 (1981), 545–546.

2. A. Berman, Book review on “Nonnegative matrices in dynamic programming”, by W.H.M. Zijm,

Siam Rev., 28 (1986), 245–246.

3. A. Berman, Book review on “Matrix analysis” by R. Horn and C.R. Johnson, Linear and Multilinear

Algebra.

Research Report

Berman, A., Dana-Pickard, N., Koichu, B., Medzinsky, S., Nahlieli, T., & Svarkman, A. (2009). Explo-

ration of the literature on secondary school mathematics programsin ﬁve countries (in Hebrew). Israel:

Ministry of Education. Retrieved January 10, 2010, from:

http ://meyda.education.gov.il/ﬁles/tochnioytLimudim/Portal/Skirot/MathSkira.pdf .

Research Problems

1. A. Berman and R. J. Plemmons, Rank factorization of nonnegative matrices, SIAM Rev., 15 (1973),

655.

2. A. Berman and M. Neumann, Monotone submatrices, SIAM Rev., 18 (1976), 490.

3732 Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734

Papers in Hebrew

1. A. Berman, Optimal programming using the arithmetic-geometric inequality, Etgar (High School

Math Journal), 3 (1978) 1–9.

2. A. Berman, Graphs, Light Bulbs and Matrices, Etgar – Gilionot Matematica (High School Math

Journal) 15 (1989), 4–11. Translated to English in Panorama – Australian High School Journal

(1990).

3. A. Berman, Arithmetic Games, Mispar Hazak (Math Elementary School Teachers Journal), 11

(2006), 26–29.

Graduate Students

Ron Aharoni 1979, Ph.D.

“Combinatorial Problems in Matrix Theory”.

Ron Adin 1981, M.Sc.

“Extreme Positive Operators on Minimal and

Almost-Minimal Cones”.

Daniel Hershkowitz 1982, Ph.D.

“Stable Matrices and Matrices with Nonnegative Principal Minors”.

Avital Livne 1983, M.Sc.

“Copositive Matrices”.

Ofra Kessler 1984, M.Sc.

“Inverse M-matrices”.

Dan Shemesh 1984, Ph.D.

“Commutativity Subspaces”.

Ron Irmai 1985, M.Sc.

“Multicriteria Decision Problems by Dynamic Programmig”.

Dafna Shasha 1987, Ph.D. (Co-Supervisor D. Hershkowitz)

“Diagonal Semistability of Matrices”.

Natali Kogan 1989, M.Sc.

“Completely Positive Matrices and Completely Positive Graphs”.

Sarel Kagan 1991, M.Sc.

“Constrained Matrix Scaling”.

Naomi Shaked Monderer 1992, Ph.D.

“Convex Sets of Positive Semideﬁnite Matrices”.

Natali Kogan 1993, Ph.D. (Co-Supervisor D. Hershkowitz)

“Combinatorial Spectral Theory”.

Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734 3733

Avi B. Sigler 1994, Ph.D.

“Geometric Investigations of High School

and Pre Service Students”.

Mark Krupnik 1994, Ph.D.

“Completion Problems in Matrix Theory”.

Marina Arab 1995, M.Sc.

“The Extended Linear Complimentarity Problem”.

Alex Kuperman 1996, Ph.D. (Co-Supervisor N. Movshovitz–Hadar)

“Misconceptions in Linear Algebra”.

Galit Dremer 1996, M.Sc.

“Seeing Mathematics”.

Roza Leikin 1997, Ph.D. (Co-Supervisor O. Zaslavsky)

“Symmetry as a Way of Thought”.

Amal Sherif Rasslan 2000, Ph.D.

University Professor as a High School Teacher–

a Case Study”.

Shmuel Aruchas 2000, M.Sc.

“Mathematical Problems that Can Be Used to

Identify Gifted Students”.

Nurit Katchalsky 2002, M.Sc.

“The Majority Rule in Graphs”.

Boris Koichu 2003, Ph.D. (Co-Supervisor M. Moore)

“Senior High School Student’s Heuristic Behaviors

in Mathematical Problem Solving”.

Sagit Ophrain 2003, M.Sc.

“Final Paper on Teaching Analytic Geometry”.

Yulia Bulgaev 2004, M.Sc.

“The Wiener Index of a Graph”.

Felix Goldberg 2004, M.Sc.

“Laplacian at Graphs, Quasi-Strongly Regular Graphs

and CompletelyPositive Praphs”.

Olga Bortnik 2004, M.Sc.

“Words in Positive Deﬁnite Matrices”.

Shmuel Aruchas 2005, Ph.D. (Co-Supervisor I. Verner)

“Applications-Motivated Calculus Course”.

3734 Editorial / Linear Algebra and its Applications 438 (2013) 3724–3734

Alon Hadad 2008, M.Sc.

“Nonnegative Matrix Factorizations”.

Shirley Medjinskey 2008, Ph.D. (Co-Supervisor R. Tal)

“Embedded Assessment in Pull-Out Programs for the Gifted”.

Felix Goldberg 2010, Ph.D.

“The Colin de Verdiere munber of a graph”.

Michal Dina 2010, M.Sc. (Co-Supervisor D. Hershkowitz)

“Spectrally arbitrary patterns”.

Yeﬁm Katz 2010, Ph.D. (Co-Supervisor B. Koichu)

“Aesthetics of Problem Solving”.

Oleg Kostenko 2010, M.Sc. (Co-Supervisor I. Baron)

“Self Adjusted Zero Trees”.

Batia Amit 2011, Ph.D. (Co-Supervisor N. Movshovitz–Hadar)

“Interweaving Mathematical Snapshots into High School Curriculum”.

Galit Hagi 2012, Ph.D. (Co-Supervisor A. Baram-Tsabary)

“Incorporating Student’s Interests into the Formal Curriculum”.

Miriam Farber M.Sc. (in progress)

Ran Peleg Ph.D. (in progress) (Co-Supervisor A. Baram-Tsabary)

Esty Laslo Ph.D. (in progress) (Co-Supervisor A. Baram-Tsabary)

Michal Klinstern Ph.D. (in progress) (Co-Supervisor B. Koichu)

Hila Gelberg Ph.D. (in progress) (Co-Supervisor B. Koichu)

Mirela Wider Ph.D. (in progress) (Co-Supervisor B. Koichu)

Salwa Mabrici M.Sc. (in progress)

Postdoctoral Students

Xiao–Dong Zhang 1998–2000

Changquing Xu 2002–2003

Shirley Medjinskey 2008–2009

Alon Levy 2010

Ayelet Baram–Tsabary 2011

Visiting Ph.D. Students

Francesco Barioli, University of Padova 2000

Rade Stansojevic, The National University of Ireland 2004

ResearchGate has not been able to resolve any citations for this publication.

A lower bound for the second largest Laplacian eigenvalue of weighted graphs

Article

Full-text available

Dec 2011
ELECTRON J LINEAR AL

Let G be a weighted graph on n vertices. Let λ n-1 (G) be the second largest eigenvalue of the Laplacian of G. For n≥3, it is proved that λ n-1 (G)≥d n-2 (G), where d n-2 (G) is the third largest degree of G. An upper bound for the second smallest eigenvalue of the signless Laplacian of G is also obtained.

More on linear inequalities with applications to matrix theory

Article

Full-text available

Mar 1971

Previous work [3, 4, 5] on solvability theorems for linear equations over cones and cones with interior is continued. Applications to matrix theory include a theorem of Bellman and Fan [2], and generalizations of Lyapunov theorem.

The Pleasure of Teaching the Gifted and the Honour of Learning from them

Chapter

Jan 2009

Combinatorial and Graph-Theoretical Problems in Linear Algebra

Book

Jan 1993

This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph~theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis.

Algebraic connectivity of trees with a pendant edge of infinite weight

Article

Jan 2005
ELECTRON J LINEAR AL

Let G be weighted graph. let v be a vertex of G and let G(omega)(v) denote the graph obtained by adding a vertex u and an edge {v, u} with weight omega to G. Then the algebraic connectivity mu(G(omega)(v)) of G(omega)(v) is a nondecreasing function of omega and is bounded by the algebraic connectivity mu(G) of G. the question of when [GRAPHICS] mu(G(omega)(v)) is equal to mu(G) is considered and answered in the case that G is a tree.

Convexity, Graph Theory and Non-Negative Matrices

Article

Dec 1984

Abraham Berman

Problems involving non-negative matrices in which both convexity and graph theory play an important role are surveyed. First, we describe work of Barker and Tam who study the irreducibility of a matrix which leaves a cone invariant via a directed graph of the faces of the cone. The second part of the paper is devoted to graph theoretical characterizations, due mainly to Brualdi, of the extreme points of various polytopes of non-negative matrices.

Complementarity Problem and Duality Over Convex Cones

Article

Jan 1974

Abraham Berman

The complementarity problem is defined and studied for cases where the constraints involve convex cones, thus extending the real and complex complementarity problems. Special cases of the problem are equivalent to dual, linear or quadratic, programs over polyhedral cones.

A generalization of irreducible monotonicity

Article

Jan 1972
LINEAR ALGEBRA APPL

Let K1 and K2 be pointed closed convex cones with nonempty interiors in Rn and Rm, respectively. Define AϵM(K1, K2) if and only if AxϵK2, 0 ≠ xϵK1, is consistent and AxϵK2, 0 ≠ xϵK1 ⇒ xϵ intK1. If K1 and K2 are the nonnegative orthants in their respective spaces, the class M(K1, K2) reduces to the class M of irreducible matrices defined by Fiedler and Ptak [7]. Properties of matrices in M are generalized for matrices in M(K1, K2). It is shown that the irreducible MK matrices, e.g., [8], is a subset of M(K, K).

Bipartite Graphs With A Central Symmetry And (1,-1)-Matrices

Article

Dec 1980

Bipartite graphs, of diameter 4, with a central symmetry are represented by equivalence classes of proper(1, -1)-matrices. This representation is used to compute the number of non-isomorphic graphs.

Generalized interval programming

Article