Special congruences of symmetric and Hermitian matrices and their invariants
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 54-60
Cet article a éte moissonné depuis la source Math-Net.Ru
Let $V_n$ be the arithmetic space of dimension $n$, and let the inner product be introduced in $V_n$ using a symmetric or a skew-symmetric involution $M$. In the resulting indefinite metric space, one can define the classes of special matrices playing the parts of symmetric, skew-symmetric, and orthogonal operators. We say that such matrices are $M$-symmetric, $M$-skew-symmetric, and $M$-orthogonal, respectively. The invariants of $M$-orthogonal congruences performed with $M$-symmetric and $M$-skew-symmetric matrices are indicated. A Hermitian counterpart of these constructions is also discussed.
@article{ZNSL_2021_504_a3,
author = {Kh. D. Ikramov},
title = {Special congruences of symmetric and {Hermitian} matrices and their invariants},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {54--60},
year = {2021},
volume = {504},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a3/}
}
Kh. D. Ikramov. Special congruences of symmetric and Hermitian matrices and their invariants. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIV, Tome 504 (2021), pp. 54-60. http://geodesic.mathdoc.fr/item/ZNSL_2021_504_a3/