Decompositions of Pseudo-Unitary and Centro-Unitary Matrices
- Authors: Ikramov K.D.1
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Affiliations:
- Moscow Lomonosov State University
- Issue: Vol 224, No 6 (2017)
- Pages: 861-868
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239700
- DOI: https://doi.org/10.1007/s10958-017-3455-8
- ID: 239700
Cite item
Abstract
ConsiderCn as the pseudo-unitary space with the inner product defined by the matrix\( {p}_n=\left(\begin{array}{l}\kern4em 1\hfill \\ {}\kern3em 1\hfill \\ {}\kern1em \dots \hfill \\ {}1\hfill \end{array}\right) \).
In this space, centro-unitary matrices play the role of unitary operators.
The main result of this paper is a factorization of an arbitrary centro-unitary matrix of even order into a product of simpler centro-unitary matrices. This result is an implication of a similar fact concerning factorizations of pseudo-unitary matrices of the type (n, n).
About the authors
Kh. D. Ikramov
Moscow Lomonosov State University
Author for correspondence.
Email: ikramov@cs.msu.su
Russian Federation, Moscow