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Linear Algebra and Its Applications
Paper

Determinant of block-Toeplitz band matrices

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Abstract

Some expressions are given for the determinant of an mn×mn block-Toeplitz band matrix L=[Li-j], with bandwidth (p+q+1)n<mn, in terms of the n×n generating matrix polynomial L(λ)=Σp+qj=0λjLp-j, detL-q≠0. In the scalar case this yields formulas for the determinant expressed via the zeros of the generating (scalar) polynomial. The approach adopted in this work leans heavily on the recently developed spectral theory of matrix polynomials. © 1987.

Date

01 Jan 1987

Publication

Linear Algebra and Its Applications

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