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The linear preservers of real diagonalizable matrices

Using a recent result of Bogdanov and Guterman on the linear preservers of pairs of simultaneously diagonalizable matrices, we determine all the automorphisms of the vector space M_n(R) which stabilize the set of diagonalizable matrices. To do so, we investigate the structure of linear subspaces of diagonalizable matrices of M_n(R) with maximal dimension.

preprint2011arXivOpen access
Bernard RandéClément de Seguins Pazzis
math.RA
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Bernard RandéClément de Seguins Pazzis

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