The Semigroup Generated by the Similarity Class of a Singular Matrix |
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| Authors: | Clément de Seguins Pazzis |
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| Institution: | 1. Lycée Privé Sainte-Geneviève , Versailles , France dsp.prof@gmail.com |
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| Abstract: | 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 ( n (𝕂), ×) 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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| Keywords: | Companion matrices Jordan canonical form Rational canonical form Semigroup Similarity class |
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