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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 854–859 (Mi mz11034)  

Checking the Congruence between Accretive Matrices

Kh. D. Ikramov

Lomonosov Moscow State University

Abstract: We call a finite computational process using only arithmetic operations a rational algorithm. A rational algorithm that is able to check the congruence between arbitrary complex matrices $A$ and $B$ is currently not known. The situation may be different if $A$ and $B$ belong to a certain class of special matrices. For instance, there exist rational algorithms for the case where both matrices are Hermitian or unitary. In this paper, rational algorithms for checking the congruence between accretive or dissipative $A$ and $B$ are proposed.

Keywords: accretive matrix, dissipative matrix, congruences, canonical form, rational algorithm.

DOI: https://doi.org/10.4213/mzm11034

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English version:
Mathematical Notes, 2017, 101:6, 969–973

Bibliographic databases:

UDC: 512.643
Received: 15.12.2015
Revised: 12.09.2016

Citation: Kh. D. Ikramov, “Checking the Congruence between Accretive Matrices”, Mat. Zametki, 101:6 (2017), 854–859; Math. Notes, 101:6 (2017), 969–973

Citation in format AMSBIB
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