Bibliographic Details
| Title: |
On normal forms for the similarity classes of matrices and pairs of matrices. |
| Authors: |
Bongartz, Klaus1 (AUTHOR) klausbongartz@online.de |
| Source: |
Linear Algebra & its Applications. Aug2026, Vol. 743, p76-86. 11p. |
| Subjects: |
Normal forms (Mathematics), Linear operators |
| Abstract: |
We answer two questions of Kontsevich posed 1998 in the book 'Arnold's problems'. First, over any field k there is a representative system for the similarity classes of n × n -matrices which is a finite disjoint union of affine subspaces. And second, for n ≥ 2 an analogous statement fails for pairs of n × n -matrices over any algebraically closed field of characteristic 0. The positive answer rests on a slight modification of the rational normal form whereas the negative answer requires more work. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
