A note on companion matrices
نویسندگان
چکیده
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. © 2003 Elsevier Inc. All rights reserved. AMS classification: 15A23; 15A57; 65F15
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