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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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Generalized Hölder's inequality for operator (subordinate) norms

While perusing the Matrix norms section of Wikipedia, I came across this generalized version of Holder's inequality. $$ \|A\|_2^2 \leq \|A \|_1 \|A \|_\infty\,, $$ where, $$ \|A \|_p = \max_{\|x\|_p …