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Appl. Math. Lett. 01/2010; 23:725-727.
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Appl. Math. Lett. 01/2010; 23:732-737.
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Appl. Math. Lett. 01/2008; 21:1199-1203.
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ABSTRACT: We give criterions for a flat portion to exist on the boundary of the numerical range of a matrix. A special type of Teoplitz matrices with flat portions on the boundary of its numerical range are constructed. We show that there exist 2 × 2 nilpotent matrices A 1,A 2, an n × n nilpotent Toeplitz matrix Nn , and an n × n cyclic permutation matrix Sn (s) such that the numbers of flat portions on the boundaries of W(A 1N n ) and W(A 2S n (s)) are, respectively, 2(n − 2) and 2n.
Linear and Multilinear Algebra 01/2008; 56(1-2):143-162. · 0.73 Impact Factor
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ABSTRACT: We deal with n-by-n matrices whose numerical ranges have ellip-tic boundary generating curves. The elliptic boundary generating curves are parametrized and classified for small n. Examples are constructed for each class. From a graph theoretical view point, we give a blockwise nilpotent Toeplitz ma-trix whose boundary generating curve has genus 1, the curve is elliptic but not rational.
International Journal of Pure and Applied Mathematics ————————————————————————– Volume. 01/2006; 30:441-465.
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ABSTRACT: Let T be a bounded linear operator on a complex Hilbert space H with inner product ·, ·. For a real number q [0, 1], the q-numerical range of T is defined by We obtain fundamental properties of the function h on conv(σ (T)) defined by If T is normal, these fundamental properties are applicable to show that Furthermore, if T is a non-essential hermitian then closure(Fq (T)) is the union of Fq (diag(λ1, λ2, λ3)) over distinct extreme points λ1, λ2, λ3 of conv(σ (T)).
Linear and Multilinear Algebra 11/2005; 53(6):393-416. · 0.73 Impact Factor
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Appl. Math. Lett. 01/2005; 18:1199-1203.
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ABSTRACT: Let T be a completely nonunitary contraction on an n-dimensional Hilbert space. Suppose that T has no eigenvalue of modulus one and . The well-known Poncelet property for numerical range W(T) shows that for any point λ on the unit circle there exists a unique (n+1)-gon, having λ as a vertex, inscribed inside the unit circle and circumscribed about W(T). We formulate the Poncelet property in terms of the boundary generating curve of W(T) and its dual form. This leads to the study of analytic continuation of unitary dilations of T.
Linear and Multilinear Algebra 05/2004; 52(3-4):159-175. · 0.73 Impact Factor
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Appl. Math. Lett. 01/2001; 14:213-216.
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Mao-Ting Chien
Appl. Math. Lett. 01/2001; 14:167-170.
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ABSTRACT: We describe the boundary of the q-numerical range of a square matrix using its Davis–Wielandt shell. The result is used to generate an algorithm for plotting the q-numerical range of the square matrix. Computations of the q-numerical ranges of a special class of matrices are explicitly given.
Linear Algebra and its Applications.
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ABSTRACT: The rank-k-numerical range of an n×n matrix A is defined asThis study presents a method to generate the boundary of Λk(A), and examines the flat portions of the boundary of the rank-k-numerical range of a matrix associated with a roulette curve. A sufficient condition is given to ensure that the rank-k-numerical range is not attainable by a classical numerical range.
Linear Algebra and its Applications 435(11):2971-2985. · 0.97 Impact Factor
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ABSTRACT: Let A be an n×n complex matrix and c=(c1,c2,…,cn) a real n-tuple. The c-numerical range of A is defined as the setWhen c=(1,0,…,0), Wc(A) becomes the classical numerical range of A which is often defined as the setW(A)={x∗Ax:x∈Cn,x∗x=1}.We show that for any n×n complex matrix A and real n-tuple c, there exists a complex matrix B of size at most n! such that Wc(A)=W(B). Constructions of the matrix B for some matrices A and real n-tuple c are provided.
Linear Algebra and its Applications.
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ABSTRACT: Let A be an n×n matrix and be a real n-tuple. The c-numerical range of A is the set is an orthonormal basis of . We obtain parametric representations of the boundary generating curve of the c-numerical range of a matrix. Applying this result, we generalize the result of Anderson to the c-numerical range. Furthermore, we give a description of the boundary generating curve of the c-numerical range of certain types of nilpotent Toeplitz matrices. A sufficient condition for the boundary generating curve to be rational is obtained. Finally we explicitly compute the boundary generating curves of the numerical ranges for several concrete matrices and classify the rationality of the curves.
Linear Algebra and its Applications.
