Geodesic
Decomposing pseudounitary and centrounitary matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 74-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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Consider $\mathbb C^n$ as the pseudounitary space with the inner product defined by the matrix $$ \mathcal P_n=\left(\begin{array}{cccc} &&&1\\ &&1&\\ &\cdots&&\\ 1&&& \end{array}\right). $$ In this space, centrounitary matrices play the role of unitary operators. The main result of this paper describes a certain factorization of an arbitrary centrounitary matrix of even order into a product of simpler centrounitary matrices. This result is an implication of a similar fact concerning factorizations of pseudounitary matrices of the type $(n,n)$. 
@article{ZNSL_2016_453_a4,
     author = {Kh. D. Ikramov},
     title = {Decomposing pseudounitary and centrounitary matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {74--84},
     year = {2016},
     volume = {453},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a4/}
}
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Kh. D. Ikramov. Decomposing pseudounitary and centrounitary matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 74-84. http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a4/