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"Matrix factorizations" is a topical category for books that center on the theory, computation and applications of expressing matrices (and higher-order arrays) as products or decompositions of simpler components. Titles in this category range from rigorous treatments of linear-algebraic decompositions—LU, QR, Cholesky, eigen/spectral and singular-value decompositions—to modern topics like low-rank approximations, nonnegative and sparse factorizations, tensor decompositions, randomized algorithms and numerical stability. They bridge pure mathematics (algebra, operator theory, algebraic geometry) and applied perspectives (machine learning, signal processing, statistics, scientific computing, control and quantum physics), and typically cover algorithm design, implementation, error analysis and real-world case studies. Such books are aimed at students, researchers and practitioners who need both the theoretical foundations and practical tools for modeling, dimensionality reduction, inverse problems and data-driven discovery.

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