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Hong's canonical form of a Hermitian matrix with respect to orthogonal *congruence.
- Source :
-
Linear Algebra & its Applications . Dec2021, Vol. 630, p241-251. 11p. - Publication Year :
- 2021
-
Abstract
- Yoopyo Hong proved in 1989 that each Hermitian matrix A is orthogonally *congruent to a matrix of the form ε 1 A 1 ⊕ ⋯ ε r A r ⊕ B 1 ⊕ ⋯ ⊕ B s , in which A 1 , ... , A r , B 1 , ... , B s are uniquely determined by the orthogonal *congruence class of A, and ε 1 , ... , ε r ∈ { 1 , − 1 }. We prove that ε 1 , ... , ε p are uniquely determined by the orthogonal *congruence class of A as well. As an application, we present a canonical form of a pair (A , B) consisting of a Hermitian matrix A and a nonsingular symmetric matrix B with respect to transformations (S ⁎ A S , S T B S) with a nonsingular S. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 630
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 152650611
- Full Text :
- https://doi.org/10.1016/j.laa.2021.08.007