On the Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form
- Autores: Ikramov K.D.1
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Afiliações:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Edição: Volume 63, Nº 2 (2023)
- Páginas: 227-229
- Seção: General numerical methods
- URL: https://edgccjournal.org/0044-4669/article/view/664888
- DOI: https://doi.org/10.31857/S0044466923020084
- EDN: https://elibrary.ru/BMSMML
- ID: 664888
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Resumo
Let A and B be Hermitian n*n matrices with A being nonsingular. According to a well-known theorem of matrix analysis, these matrices can be brought to diagonal form by one and the same Hermitian congruence transformation if and only if the matrix C = A-1B has a real spectrum and can be diagonalized by a similarity. An extension of this assertion to the case where two unitoid matrices are simultaneously reduced to diagonal form is stated and proved.
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Sobre autores
Kh. Ikramov
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Autor responsável pela correspondência
Email: ikramov@cs.msu.su
Moscow, Russia
Bibliografia
- Horn R.A., Johnson C.R. Matrix Analysis. Cambridge: Cambridge University Press, 1985.
- Икрамов Х.Д. К опыту спектральной теории для преобразований эрмитовой конгруэнции // Зап. научн. сем. ПОМИ. 2019. Т. 482. С. 114–119.
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