Equality conditions for the singular values of 3 × 3 matrices with one-point spectrum |
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Authors: | Kh. D. Ikramov |
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Affiliation: | (1) M. V. Lomonosov Moscow State University, Moscow |
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Abstract: | Let Γa be an upper triangular 3 × 3 matrix with diagonal entries equal to a complex scalar a. Necessary and su.cient conditions are found for two of the singular values of Γa to be equal. These conditions are much simpler than the equality discr ? = 0, where the expression in the left-hand side is the discriminant of the characteristic polynomial ? of the matrix Ga = ΓaΓa. Understanding the behavior of singular values of Γa is important in the problem of finding a matrix with a triple zero eigenvalue that is closest to a given normal matrix A. |
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Keywords: | upper triangular matrix singular value of a matrix spectral distance normal matrix characteristic equation |
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