The linear preservers of real diagonalizable matrices

Details The linear preservers of real diagonalizable matrices The linear preservers of real diagonalizable matrices

2010-07-12

arxiv.org/abs/1007.1983v3

Linear Algebra Appl. 435-6 (2011) pp.1257-1266

Mathematics

Rings and Algebras

14 pages

Scientific paper

10.1016/j.laa.2011.03.014

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.

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