Lecture Notes of Matrix Computations by Wen Wei Lin
Lecture Notes of Matrix Computations - Table of Contents
PART I: DIRECT METHODS & FACTORIZATIONS
- 1. Basic Matrix Concepts and Floating-Point Arithmetic
- 2. LU Factorization and Gaussian Elimination
- 3. Cholesky Factorization for Positive Definite Matrices
- 4. Householder Transformations and Givens Rotations
- 5. QR Decomposition and Linear Least Squares
PART II: EIGENVALUES & ITERATIVE METHODS
- 6. Singular Value Decomposition (SVD) and Applications
- 7. Symmetric and Non-Symmetric Eigenvalue Problems
- 8. The QR Algorithm and Hessenberg Reduction
- 9. Lanczos and Arnoldi Krylov Subspace Methods
- 10. Structure-Preserving Algorithms for Matrix Equations
What You Will Learn in Lecture Notes of Matrix Computations
Lecture Notes of Matrix Computations by Wen-Wei Lin is an authoritative, advanced lecture series that provides a systematic and mathematically rigorous foundation in numerical matrix analysis and algorithm design. This comprehensive volume guides readers through direct methods, LU and Cholesky factorizations, QR decompositions, Householder transformations, singular value decomposition (SVD), and Krylov subspace methods with exceptional analytical precision.
Designed for graduate students, computational mathematicians, scientific programmers, and numerical analysis researchers, this foundational text bridges abstract linear algebra and high-performance scientific computing. Lin presents step-by-step stability analysis, floating-point error estimates, and convergence proofs for symmetric and non-symmetric matrix eigensolvers. Whether you are developing numerical software, solving large linear systems, or investigating structure-preserving matrix algorithms, this text offers an indispensable roadmap.
Recognized globally for its clear mathematical exposition and pedagogical structure, it remains one of the best matrix computation lecture notes for self-study. By balancing theoretical matrix analysis with practical algorithmic design, it serves as an essential tool for mastering numerical matrix computations with confidence.
Book Details & Specifications
Title:
Lecture Notes of Matrix Computations by Wen Wei Lin
Publisher:
National Tsing Hua University, Hsinchu, Taiwan
Year:
2010
Pages:
339
Type:
PDF
Language:
English
ISBN-10 #:
0126703507
ISBN-13 #:
978-0126703504
License:
University Educational Resource
Amazon:
Amazon
About the Author: Wen-Wei Lin
The author Wen-Wei Lin
is a distinguished Chair Professor of Applied Mathematics at National Chiao Tung University (NCTU) in Taiwan, internationally celebrated for his foundational contributions to numerical linear algebra, Hamiltonian matrix computations, quantum dot simulations, and scientific computing. He earned his doctorate in applied mathematics from the Center for Applied Mathematics at the University of Darmstadt, Germany, and has published hundreds of influential research papers in top-tier numerical analysis journals.
Developed from decades of advanced university instruction, Lin authored Lecture Notes of Matrix Computations to offer students a clean, rigorous, and algorithmically sound path through complex numerical methods. His focus on structural preservation, numerical stability, and clear step-by-step proofs makes this text a classic reference for numerical linear algebra algorithms that continues to be relied upon by computational scientists worldwide.
Read or Downloadable Lecture Notes of Matrix Computations
Free Matrix Algebra Books PDF - Linear & Matrix Methods