Vector-monotonicity of a symmetric eigenvalue function is equivalent to matrix-monotonicity of the induced isotropic tensor function, with strict versions, invertibility criteria, and consequences for the Baker-Ericksen inequalities.
Another Simple Proof of a Theorem of Chandler Davis
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In 1957, Chandler Davis proved that unitarily invariant convex functions on the space of hermitian matrices are precisely those which are convex and symmetrically invariant on the set of diagonal matrices. We give a simple perturbation theoretic proof of this result. (Davis' argument was also very short, though based on completely different ideas).
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Monotonicity of isotropic tensor functions on the set of symmetric matrices: completing Rodney Hill's generalization of the Chandler Davis convexity theorem
Vector-monotonicity of a symmetric eigenvalue function is equivalent to matrix-monotonicity of the induced isotropic tensor function, with strict versions, invertibility criteria, and consequences for the Baker-Ericksen inequalities.