Determinants of block tridiagonal matrices

Dipartimento di Fisica, Università degli Studi di Milano and INFN, Sezione di Milano, Via Celoria 16, Milano, Italy
Linear Algebra and its Applications (Impact Factor: 0.97). 01/2008; DOI: 10.1016/j.laa.2008.06.015
Source: arXiv

ABSTRACT An identity is proven that evaluates the determinant of a block tridiagonal matrix with (or without) corners as the determinant of the associated transfer matrix (or a submatrix of it).

1 Bookmark
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The formulas presented in [Molinari, L.G. Determinants of block tridiagonal matri-ces. Linear Algebra Appl., 2008; 429, 2221–2226] for evaluating the determinant of block tridiagonal matrices with (or without) corners are used to derive the determinant of any multidiagonal matri-ces with (or without) corners with some specified non-zero minors. Algorithms for calculation the determinant based on this method are given and properties of the determinants are studied. Some applications are presented.
    The electronic journal of linear algebra ELA 11/2012; 25:101-117. · 0.89 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free form of a linear code and its dual code over a Hamming scheme. In this paper we find a new explicit expression for the -number and the -number, which are more generalized notions of the Krawtchouk polynomial in the P-polynomial schemes by using an extended version of a discrete Green's function. As corollaries, we obtain a new expression of the Krawtchouk polynomial over the Hamming scheme and the Eberlein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme.
    Journal of the Korean Mathematical Society 01/2013; 50(3). · 0.32 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Recently, three computational algorithms for evaluating the determinant of quasi penta-diagonal matrices have been proposed by El-Mikkawy and Rahmo (Comput Math Appl 59:1386–1396, 2010), by Neossi Nguetchue and Abelman (Appl Math Comput 203:629–634, 2008), and by Jia et al. (Int J Comput Math 89:851–860, 2013), respectively. In the current paper, two novel algorithms with less computational costs are proposed for the determinant evaluation of general quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices. Furthermore, three numerical experiments are given to show the performance of our algorithms. All of the numerical computations were performed on a computer with aid of programs written in MATLAB.
    Journal of Mathematical Chemistry 01/2013; · 1.23 Impact Factor

Full-text (2 Sources)

Available from
May 22, 2014