Matrix identities involving multiplication and transposition

Abstract

We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.

35 pages, 1 figure. This paper has grown from the first part of the authors' preprint 0902.1155 (entitled "Equational theories of semigroups with enriched signature"). It focuses on the finite basis problem for matrix indentities involving multiplication and unary operations such as transposition or symplectic transpose or Moore-Penrose inversion

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