On properties of quadratic matrices (Q2714289)
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 properties of quadratic matrices |
scientific article; zbMATH DE number 1604181
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On properties of quadratic matrices |
scientific article; zbMATH DE number 1604181 |
Statements
13 June 2001
0 references
projection
0 references
involution
0 references
eigenvalues
0 references
singular values
0 references
numerical range
0 references
inverse eigenproblem
0 references
Moore-Penrose inverse
0 references
On properties of quadratic matrices (English)
0 references
A matrix \(A\) over \(\mathbb C\) is said to be a quadratic matrix if there exist \(p,q\in\mathbb C\) such that \((A-pI)(A-qI)=0\) where \(I\) is the identity matrix. Properties of quadratic matrices are derived. The inverse eigenproblem of quadratic matrices is considered, and it is shown how to find a quadratic matrix with prescribed singular values. The Moore-Penrose inverse of a quadratic matrix is determined, and the authors find the closest normal matrix to a quadratic matrix in the 2-norm and the Frobenius norm. The case of elementary matrices is considered, and a characterization of the numerical range of quadratic matrices is given.
0 references
