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A note on companion matrices

✍ Scribed by Miroslav Fiedler

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 82 KB
Volume: 372
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00548-2

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✦ Synopsis

We show that the usual companion matrix of a polynomial of degree n can be factored into a product of n matrices, n -1 of them being the identity matrix in which a 2 × 2 identity submatrix in two consecutive rows (and columns) is replaced by an appropriate 2 × 2 matrix, the remaining being the identity matrix with the last entry replaced by possibly different entry. By a certain similarity transformation, we obtain a simple new companion matrix in a pentadiagonal form. Some generalizations are also possible.

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