Simultaneously Diagonalizable Matrices and the Congruence Analog of the Commutativity Property

— It is well known that if diagonalizable matrices and commute, then they can be brought to diagonal form by one and the same similarity transformation. We prove an analog of this assertion concerning nonsingular unitoid matrices and transformations of Hermitian congruence. A matrix is said to be un...

Full description

Saved in:
Bibliographic Details
Published inNumerical analysis and applications Vol. 18; no. 3; pp. 237 - 241
Main Author Ikramov, Kh. D.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.09.2025
Springer Nature B.V
Subjects
Commutativity
Conflicts of interest
Congruences
Eigenvalues
Equality
Mathematics
Mathematics and Statistics
Numerical Analysis
Orbits
canonical form with respect to congruences
unitoid
congruence orbit
cosquare
canonical angles
Online AccessGet full text
ISSN1995-4239
1995-4247
DOI10.1134/S1995423925030048

Cover

More Information
Summary:— It is well known that if diagonalizable matrices and commute, then they can be brought to diagonal form by one and the same similarity transformation. We prove an analog of this assertion concerning nonsingular unitoid matrices and transformations of Hermitian congruence. A matrix is said to be unitoid if it can be brought to diagonal form by congruences.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423925030048