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Singular value inequalities for the arithmetic, geometric and Heinz means of matrices. (English) Zbl 1242.15015
Given two complex matrices: $$A$$ being positive definite and $$B$$ being positive semidefinite, for $$\nu \in [0,1]$$, the matrix $$(1-\nu)A+\nu B$$ is called the $$\nu$$-weighted arithmetic mean of $$A$$ and $$B$$; and $$A\sharp_\nu B := A^{1/2}( A^{-1/2}B A^{-1/2})^\nu A^{1/2}$$ is called the $$\nu$$-weighted geometric mean of $$A$$ and $$B$$, moreover, $$H_\nu(A,B) := (A\sharp_\nu B + A\sharp_{1-\nu} B)/2$$ is called the $$\nu$$-weighted Heinz mean of $$A$$ and $$B$$. In this paper, several singular value inequalities for matrix expressions involving those means are obtained. Furthermore, some applications of these results are provided.

##### MSC:
 15A42 Inequalities involving eigenvalues and eigenvectors 15B48 Positive matrices and their generalizations; cones of matrices 26E60 Means 47A64 Operator means involving linear operators, shorted linear operators, etc.
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##### References:
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