Eigenvalue inequalities associated with the cartesian decomposition

Bhatia, R. ; Ando, T. (1987) Eigenvalue inequalities associated with the cartesian decomposition Linear and Multilinear Algebra, 22 (2). pp. 133-147. ISSN 0308-1087

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0308108...

Related URL: http://dx.doi.org/10.1080/03081088708817828

Abstract

Let T=A+iB where A B are Hermitian matrices. We obtain several inequalities relating the lp distance between the eigenvalues of A and those of iB with the Schatten p-norm of T. The majorization results which lead to these inequalities are also used to get simple proofs of some known lower and upper bounds for the determinant of T.

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