On some pentadiagonal matrices:
their determinants and inverses

Abstract. In this paper we consider pentadiagonal \((n+1)\times(n+1)\) matrices with two super-diagonals and two sub-diagonals at distances \(k\) and \(2k\) from the main diagonal. We give an explicit formula for their determinants provided that \((n+1)/3\le k\le n/2.\) We consider the Toeplitz and “imperfect” Toeplitz versions of such matrices, and give explicit formulas for their determinants. We also show that the inverse matrix can be obtained as the product of an upper triangle matrix with two super-diagonals, a diagonal and a lower triangle matrix with two sub-diagonals.

Key words and phrases. Toeplitz matrix, pentadiagonal, tridiagonal matrices.