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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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Condition for the integrability of a matrix function

Can we find the sufficient and necessary condition of $a$, $b$ and $c$ $\in\mathbb R_+$ such that the following integration is integrable? $$ I_1\equiv\int \frac{1}{|\Sigma|^a|\Xi|^b|\mathrm{L}\Sigma\ …