Pseudo-Orthogonal Eigenvalues of Skew-Symmetric Matrices
- Autores: Ikramov K.1
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Afiliações:
- Lomonosov Moscow State University
- Edição: Volume 240, Nº 6 (2019)
- Páginas: 765-768
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/242831
- DOI: https://doi.org/10.1007/s10958-019-04393-9
- ID: 242831
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Resumo
The following result is attributed to J. Williamson: Every real, symmetric, and positive definite matrix A of even order n = 2m can be brought to diagonal form by a congruence transformation with symplectic matrix. The diagonal entries of this form are invariants of congruence transformations performed with A, and they are called the symplectic eigenvalues of this matrix. This short paper proves an analogous fact concerning (complex) skew-symmetric matrices and transformations belonging to a different group, namely, the group of pseudo-orthogonal matrices.
Sobre autores
Kh. Ikramov
Lomonosov Moscow State University
Autor responsável pela correspondência
Email: ikramov@cs.msu.su
Rússia, Moscow