Abstract

Factorization of orthogonal block circulant matrices can not be generalized in a straightforward way for block circulant matrices which are merely invertible. However, they can be decomposed into an orthogonal matrix and an atom that represents the `nonorthogonal' part of the matrix. Atoms can be characterized by nilpotent block-companion matrices. This characterization permits, for example, to derive bounds for the width of the band of the inverse of a banded block circulant matrix.

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