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Some New Characterizations of a Hermitian Matrix and Their Applications.
- Source :
- Complex Analysis & Operator Theory; Jan2024, Vol. 18 Issue 1, p1-8, 8p
- Publication Year :
- 2024
-
Abstract
- A square matrix A over the field of complex numbers is said to be Hermitian if A = A ∗ , the conjugate transpose of A, while Hermitian matrices are known to be an important class of matrices. In addition to the definition, a Hermitian matrix can be characterized by some other matrix equalities. This fact can be described in the implication form f (A , A ∗) = 0 ⇔ A = A ∗ , where f (·) denotes certain ordinary algebraic operation of A and A ∗ . In this note, we show two special cases of the equivalent facts: A A ∗ A = A ∗ A A ∗ ⇔ A 3 = A A ∗ A ⇔ A = A ∗ without assuming the invertibility of A through the skillful use of decompositions and determinants of matrices. Several consequences and extensions are presented to a selection of matrix equalities composed of multiple products of A and A ∗ . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16618254
- Volume :
- 18
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Complex Analysis & Operator Theory
- Publication Type :
- Academic Journal
- Accession number :
- 173714430
- Full Text :
- https://doi.org/10.1007/s11785-023-01440-x