Effective algorithms for decomplexifying a matrix by unitary similarities or congruences |
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Authors: | Kh D Ikramov |
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Institution: | 1. Moscow State University, Moscow, Russia
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Abstract: | It is required to verify whether a given complex n × n matrix A can be made real by a similarity or a congruence transformation. Algorithms for solving these two problems are proposed and justified under the additional assumption that A is irreducible in the former case and $A_L = \bar AA$ is irreducible in the latter case. The irreducibility of a square complex matrix means that no unitary similarity transformation converts this matrix into a direct sum of smaller matrices. The proposed algorithms are effective in the sense that their implementation requires a finite number of arithmetic operations. |
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