The semigroup generated by the similarity class of a singular matrix

Details The semigroup generated by the similarity class of a singular matrix The semigroup generated by the similarity class of a singular matrix

2011-01-03

arxiv.org/abs/1101.0549v2

Mathematics

Rings and Algebras

8 pages

Scientific paper

Let A be a singular matrix of M_n(K), where K is an arbitrary field. Using
canonical forms, we give a new proof that the sub-semigroup of (M_n(K),x)
generated by the similarity class of A is the set of matrices of M_n(K) with a
rank lesser than or equal to that of A.

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