Pseudo-Orthogonal Eigenvalues of Skew-Symmetric Matrices
- Авторы: Ikramov K.1
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Учреждения:
- Lomonosov Moscow State University
- Выпуск: Том 240, № 6 (2019)
- Страницы: 765-768
- Раздел: 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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Аннотация
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.
Об авторах
Kh. Ikramov
Lomonosov Moscow State University
Автор, ответственный за переписку.
Email: ikramov@cs.msu.su
Россия, Moscow