The singular linear preservers of non-singular matrices |
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Authors: | Clé ment de Seguins Pazzis |
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Affiliation: | Lycée Privé Sainte-Geneviève, 2, rue de l’École des Postes, 78029 Versailles Cedex, France |
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Abstract: | Given an arbitrary field K, we reduce the determination of the singular endomorphisms f of Mn(K) such that f(GLn(K))⊂GLn(K) to the classification of n-dimensional division algebras over K. Our method, which is based upon Dieudonné’s theorem on singular subspaces of Mn(K), also yields a proof for the classical non-singular case. |
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Keywords: | 15A86 15A30 16S50 |
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