Singular value inequalities of matrix sum in log-majorizations. (English) Zbl 1512.15020
Summary: We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices. The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two positive semidefinite matrices. Besides, we state explicitly Hoffman’s minimax theorem with a proof, and as applications of our main results, we revisit and give estimates for related determinant inequalities of Hua type.
MSC:
| 15A42 | Inequalities involving eigenvalues and eigenvectors |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
eigenvalue; Hoffman minimax theorem; Hua determinant inequality; log-majorization; majorization; Minkowski determinant inequality; singular value; Wielandt minimax theoremReferences:
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