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Numerical linear algebra as a book category covers the theory, algorithms, and practical implementation of methods for solving and analyzing matrix and vector problems that arise in scientific computing, data analysis, and engineering. Typical topics include direct and iterative methods for linear systems, eigenvalue and singular value decompositions, matrix factorizations (LU, QR, Cholesky), Krylov subspace and multigrid methods, preconditioning, sparse and structured matrix techniques, and modern randomized and low-rank approximation algorithms. Emphasis is placed on numerical stability, error and conditioning analysis, computational complexity, and efficient software/parallel implementations for large-scale problems. Books in this category range from advanced undergraduate introductions to graduate-level and reference texts aimed at mathematicians, computational scientists, and practitioners in machine learning, signal processing, and engineering who need reliable, high-performance linear algebra tools.

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