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.
Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids
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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.