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"Matrix Decompositions" as a book category encompasses works that develop, analyze, and apply methods for representing matrices as products or sums of simpler, structured factors—examples include eigendecomposition, singular value decomposition (SVD), LU/Cholesky/QR factorizations, Schur and Jordan forms, and modern variants for sparse or structured matrices. Books in this category range from theoretical treatments (existence, uniqueness, spectral theory and perturbation analysis) to practical texts on numerical algorithms, stability, and efficient implementation on modern hardware, and to application-driven volumes showing how decompositions enable dimensionality reduction, signal processing, statistical inference, machine learning, control, and scientific computing. Typical readers include advanced undergraduates, graduate students, researchers, and engineers who need both mathematical foundations and computational techniques, and the works often cover prerequisites (linear algebra, numerical analysis), software libraries, and case studies demonstrating real-world use.

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