Is every nonsingular matrix diagonally equivalent to a matrix with all distinct eigenvalues?
| Autor: | Xin-Lei Feng, Ting-Zhu Huang, Zhongshan Li |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Numerical Analysis
Hollow matrix Algebra and Number Theory Square root of a 2 by 2 matrix Diagonalizability Single-entry matrix Distinct eigenvalues Resultant Combinatorics Matrix function Discrete Mathematics and Combinatorics Nonnegative matrix Geometry and Topology Involutory matrix Centrosymmetric matrix Nonsingular matrix Diagonal equivalence Discriminant Diagonally dominant matrix Mathematics |
| Zdroj: | Linear Algebra and its Applications. 436(1):120-125 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2011.06.032 |
| Popis: | It is shown that a 2 × 2 complex matrix A is diagonally equivalent to a matrix with two distinct eigenvalues iff A is not strictly triangular. It is established in this paper that every 3 × 3 nonsingular matrix is diagonally equivalent to a matrix with 3 distinct eigenvalues. More precisely, a 3 × 3 matrix A is not diagonally equivalent to any matrix with 3 distinct eigenvalues iff det A = 0 and each principal minor of A of order 2 is zero. It is conjectured that for all n ⩾ 2 , an n × n complex matrix is not diagonally equivalent to any matrix with n distinct eigenvalues iff det A = 0 and every principal minor of A of order n - 1 is zero. |
| Databáze: | OpenAIRE |
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