Journal of the European Mathematical Society

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Volume 14, Issue 3, 2012, pp. 937–969
DOI: 10.4171/JEMS/323

Published online: 2012-03-07

Matrix identities involving multiplication and transposition

Karl Auinger[1], Igor Dolinka[2] and Mikhail V. Volkov[3]

(1) Universität Wien, Austria
(2) University Novi Sad, Serbia
(3) Ural Federal University, Ekaterinburg, Russian Federation

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.

Keywords: Matrix transposition, symplectic transpose, Moore–Penrose inverse, matrix law, identity basis, finite basis problem

Auinger Karl, Dolinka Igor, Volkov Mikhail: Matrix identities involving multiplication and transposition. J. Eur. Math. Soc. 14 (2012), 937-969. doi: 10.4171/JEMS/323