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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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Low-rank approximation of sub-sampled matrix
Considering a large data matrix $X$ with zero-centered columns that is assumed to be approximately low-rank, it is common to do PCA and project the data onto the top few principal components, and use …