Advanced Linear Algebra: Foundations to Frontiers by Robert van de Geijn
Advanced Linear Algebra: Foundations to Frontiers - Table of Contents
0. Getting Started
PART-I ORTHOGONALITY
- 1. Norms
- 2. The Singular Value Decomposition
- 3. The QR Decomposition
- 4. Linear Least Squares
PART-II SOLVING LINEAR SYSTEMS
- 5. The LU and Cholesky Factorizations
- 6. Numerical Stability
- 7. Solving Sparse Linear Systems
- 8. Descent Methods
PART-III THE ALGEBRAIC EIGENVALUE PROBLEM
- 9. Eigenvalues and Eigenvectors
- 10. Practical Solution of the Hermitian Eigenvalue Problem
- 11. Computing the SVD
- 12. Attaining High Performance
What You Will Learn in Advanced Linear Algebra: Foundations to Frontiers
Advanced Linear Algebra: Foundations to Frontiers by Robert van de Geijn and Maggie Myers is a groundbreaking open textbook connecting linear algebra theory directly with high-performance computing algorithms. Serving as a modern university-level reference, this volume provides a robust framework for advanced linear algebra problem solving practice.
The book systematically covers vector spaces, linear transformations, matrix-vector operations, Gaussian elimination, LU decomposition, QR factorization, orthogonality, and Hermitian eigenvalue problems. By combining rigorous mathematical proof with algorithmic notation, Geijn and Myers enable students to execute essential matrix decompositions and numerical linear transformations with absolute confidence.
Widely acclaimed in computer science and applied mathematics programs for its systematic algorithmic approach, structured notation, and practical exercise sets, this open-access resource serves as an outstanding self-study guide. The authors’ modern pedagogy equips learners with vital quantitative tools required for mastering modern computational linear algebra principles.
Book Details & Specifications
Title:
Advanced Linear Algebra: Foundations to Frontiers by Robert van de Geijn
Publisher:
University of Texas
Year:
2022
Pages:
643
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
CC BY-SA 2.5
Amazon:
Amazon
About the Author: Robert van de Geijn
The author Robert van de Geijn
is a Professor of Computer Science at the Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin, renowned for his research in high-performance linear algebra libraries (FLAME/BLIS).
His collaboration with Maggie Myers has yielded world-class advanced linear algebra and numerical computing study guides.
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