Determinants of multidiagonal matrices

Abstract

The formulas presented in [Molinari, L.G. Determinants of block tridiagonal matrices. 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 matrices 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.