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Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.

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The sum of squared logarithms conjecture

The article http://arxiv.org/abs/1410.2706 by Neff and Pompe gives a criterion, for which functions the partial derivative with respect to the elementary symmetric polynomials is nonnegative (and chec …
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