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On the Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form
- Authors: Ikramov K.D.1
-
Affiliations:
- Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
- Issue: Vol 63, No 2 (2023)
- Pages: 227-229
- Section: General numerical methods
- URL: https://rjpbr.com/0044-4669/article/view/664888
- DOI: https://doi.org/10.31857/S0044466923020084
- EDN: https://elibrary.ru/BMSMML
- ID: 664888
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Abstract
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.
About the authors
Kh. D. Ikramov
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University
Author for correspondence.
Email: ikramov@cs.msu.su
Moscow, Russia
References
- 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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