Abstract
Let A be a square matrix of order n whose entries are rational or rational Gaussian numbers. A method is described that verifies the possibility of diagonalizing A by means of congruence and uses a finite number of arithmetic (and, in the complex case, conjugation) operations.
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References
R. A. Horn and Ch. R. Johnson, Matrix Analysis. Second Edition (Cambridge: Cambridge University Press, 2012).
A. G. Kurosh. A Course of Higher Algebra (Moscow, Fizmatgis, 1963) [in Russian].
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Original Russian Text © Kh.D. Ikramov, 2016, published in Vestnik Moskovskogo Universiteta, Seriya 15: Vychislitel’naya Matematika i Kibernetika, 2016, No. 2, pp. 3–5.
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Ikramov, K.D. A finite rational algorithm that verifies the diagonalizability of a square matrix by congruence. MoscowUniv.Comput.Math.Cybern. 40, 53–56 (2016). https://doi.org/10.3103/S0278641916020059
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DOI: https://doi.org/10.3103/S0278641916020059