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 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).

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    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.
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