Two classes of matrices with fast computable spectra (Q749155)
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: Two classes of matrices with fast computable spectra |
scientific article; zbMATH DE number 4172253
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two classes of matrices with fast computable spectra |
scientific article; zbMATH DE number 4172253 |
Statements
Two classes of matrices with fast computable spectra (English)
0 references
1989
0 references
Two classes of real \(n\times n\)-matrices are defined where all the eigenvalues can be calculated in \(O(n^ 2)\) arithmetic operations. The first class consists of the Caley transforms \((I-A)(I+A)^{-1}\) of all skew-symmetric tridiagonal matrices A, the second of the Caley transforms of all orthogonal upper Hessenberg matrices with positive subdiagonal and \(\det (I+A)\neq 0\). Simple algorithms for recognizing that a matrix belongs to one of these classes are also given.
0 references
tridiagonal orthogonal matrices
0 references
eigenvalues
0 references
Caley transforms
0 references
skew- symmetric tridiagonal matrices
0 references
Hessenberg matrices
0 references
algorithms
0 references
