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Some equalities in a unitary space leading to equalities concerning singular values of sets of matrices. (English) Zbl 0082.24406

MSC:
15A18 Eigenvalues, singular values, and eigenvectors
15A24 Matrix equations and identities
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References:
[1] Amir-Moéz, A. R.: Extreme properties of Eigenvalues of a Hermitian transformation and singular values of sum and product of linear transformations. Duke Math. J.23, 463-476. · Zbl 0071.01601
[2] Amir-Moéz, A. R., andA. Horn: Singular values of a matrix; to appear in Amer. math. Monthly. · Zbl 0084.01801
[3] Ky Fan, andA. J. Hoffman: Some metric inequalities in the space of matrices. Proc. Amer. math. Soc.6, 111-116 (1955). · Zbl 0064.01402 · doi:10.1090/S0002-9939-1955-0067841-7
[4] Horn, A.: On the Eigenvalues of a matrix with prescribed singular values. Proc. Amer. math. Soc.5, No. 1, pp. 4-7 (1954). · Zbl 0055.00908 · doi:10.1090/S0002-9939-1954-0061573-6
[5] Schur, I.: Über eine Klasse von Mittelbildungen mit Anwendungen aus der Determinantentheorie. S.-B. Berlin math. Ges.22, 9-20 (1923). · JFM 49.0054.01
[6] Weyl, H.: Inequalities between the two kinds of Eigenvalues of a linear transformation. Proc. nat. Acad. Sci. (Wash.)35, 408-411 (1949). · Zbl 0032.38701 · doi:10.1073/pnas.35.7.408
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