Abstract. We investigate whether variants of equivalence of (singular) matrix polynomials imply those of the first companion linearizations, and the converse question. We study a method of deciding whether two polynomials are strictly equivalent, and which are all the pairs of matrices effecting this equivalence. The corresponding problems for the (strict) similarity of square matrix polynomials are studied. We investigate the strict equivalence of a square polynomial to a polynomial whose all coefficient matrices are diagonal, and study also the singular case.

DOI: 10.14232/actasm-012-012-z

AMS Subject Classification (1991): 47A56, 15A22

Keyword(s): singular matrix polynomial, companion linearization, equivalence, strong and strict equivalence, similarity, strictly diagonizable, (block) diagonally strict equivalence

Received February 22, 2012, and in revised form April 5, 2012. (Registered under 12/2012.)