On the number of invariant polynomials of matrix commutators (Q1361837)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the number of invariant polynomials of matrix commutators |
scientific article; zbMATH DE number 1040640
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of invariant polynomials of matrix commutators |
scientific article; zbMATH DE number 1040640 |
Statements
On the number of invariant polynomials of matrix commutators (English)
0 references
22 March 1998
0 references
For a matrix \(A\in F^{n\times n}\), \(F\) being a field, let \(i(A)\) denote a number of nonconstant invariant polynomials of \(A\). Given \(A\), the author solves the problem of characterizing the possible values of \(i(XA- AX)\) when \(X\) varies, assuming that all the irreducible polynomials in \(F(x)\) have degree \(\leq 2\). In particular, the problem is solved for algebraically closed fields and for the field \(\mathbb{R}\) of real numbers.
0 references
matrix commutator
0 references
invariant polynomials
0 references
irreducible polynomials
0 references
0 references
