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arXiv · 2502.10926

On normal forms for the similarity classes of matrices and pairs of matrices

Klaus Bongartz
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Abstract

We answer two questions posed 1998 in the book 'Arnolds problems'. First, over any field k there is a representative system for the similarity classes of nxn-matrices which is a finite disjoint union of affine subspaces. And second, for n>1 an analogous statement fails for pairs of nxn-matrices over any algebraically closed field of characteristic 0.

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Klaus Bongartz. 2025-02-15. On normal forms for the similarity classes of matrices and pairs of matrices. https://arxiv.org/abs/2502.10926

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