Displaying similar documents to “Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring”

An inverse matrix of an upper triangular matrix can be lower triangular

Waldemar Hołubowski (2002)

Discussiones Mathematicae - General Algebra and Applications

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In this note we explain why the group of n×n upper triangular matrices is defined usually over commutative ring while the full general linear group is defined over any associative ring.

Conjugacy and factorization results on matrix groups

Thomas Laffey (1994)

Banach Center Publications

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In this survey paper, we present (mainly without proof) a number of results on conjugacy and factorization in general linear groups over fields and commutative rings. We also present the additive analogue in matrix rings of some of these results. The first section deals with the question of expressing elements in the commutator subgroup of the general linear group over a field as (simple) commutators. In Section 2, the same kind of problem is discussed for the general linear group over...