NUMERICAL LINEAR ALGEBRA Theory, Algorithms, and Applications : A Complete University-Level Textbook for Mathematics, Engineering, Data Science, AI, and Scientific Computing
English | June 10, 2026 | ASIN: B0H4QCB58T | 333 pages | Epub | 10.23 MB
Master Numerical Linear Algebra with ConfidenceNumerical Linear Algebra is the foundation of modern scientific computing, engineering simulation, machine learning, data science, optimization, and artificial intelligence. This comprehensive university-level textbook provides a rigorous yet accessible introduction to the theory, algorithms, and real-world applications that power today's computational technologies.Designed for undergraduate and graduate students in mathematics, engineering, computer science, data science, and related fields, this book bridges the gap between theoretical linear algebra and practical numerical computation. Readers will learn not only how algorithms work, but also why they work, when they fail, and how to analyze their accuracy, stability, and efficiency.Inside this book, you will learn:* Floating-point arithmetic and round-off error analysis* Vector and matrix norms* Conditioning and sensitivity analysis* Gaussian elimination and LU factorization* Cholesky and QR factorizations* Eigenvalue and eigenvector algorithms* Singular Value Decomposition (SVD)* Least-squares methods* Iterative methods for large linear systems* Krylov subspace techniques and Conjugate Gradient methods* Sparse matrix computations* Matrix computations in machine learning and AI* Randomized numerical linear algebra* Tensor computations and advanced topics* Python and MATLAB implementationsThis textbook features:clear explanations and intuitive insights Step-by-step worked examples Computational complexity analysis Practical engineering and scientific applications Python and MATLAB programming examples End-of-chapter exercises and projects Modern coverage of AI, machine learning, and large-scale computingWhether you are taking a university course, preparing for graduate studies, conducting research, or developing advanced computational skills for industry applications, this book provides the essential tools needed to understand and apply numerical linear algebra with confidence.Build a strong foundation in one of the most important subjects in modern computational science and engineering.
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