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Considering n×n×n stochastic tensors (aijk) (i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex set (Ln) of all tensors in Ωn with some positive diagonals, and the polytope (Δn) generated by the permutation tensors. We show that Ln is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn. [ABSTRACT FROM AUTHOR]

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor products of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a multilinear approach, we show some matrix inequalities concerning induced operators and generalized matrix functions (including determinants and permanents as special cases). [ABSTRACT FROM AUTHOR]

We present inequalities concerning the entries of correlation matrices, density matrices, and partial isometries through the positivity of 3 × 3 matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive functions. [ABSTRACT FROM AUTHOR]

By using representation theory and irreducible characters of the symmetric group, we introduce character dependent states and study their entanglement via geometric measure. We also present a geometric interpretation of generalized matrix functions via this entanglement analysis. [ABSTRACT FROM AUTHOR]

Abstract: We show some majorization inequalities and apply them to derive norm, eigenvalue, singular value, and trace inequalities of matrices. We also present a generalization and a different proof of a recent result on majorization concerning partitioned Hermitian positive semidefinite matrices. [Copyright &y& Elsevier]