Linear Algebra: Foundations to Frontiers by M.E. Myers
Linear Algebra: Foundations to Frontiers - Table of Contents
0. Notes on Setting Up
1. Notes on Simple Vector and Matrix Operations
2. Notes on Vector and Matrix Norms
3. Notes on Orthogonality and the Singular Value Decomposition
4. Notes on Gram-Schmidt QR Factorization
5. Notes on the FLAME APIs Algorithms
6. Notes on Householder QR Factorization
7. Notes on Rank Revealing Householder QR Factorization
8. Notes on Solving Linear Least-Squares Problems
9. Notes on the Condition of a Problem
10. Notes on the Stability of an Algorithm
11. Notes on Performance
12. Notes on Gaussian Elimination and LU Factorization
13. Notes on Cholesky Factorization
14. Notes on Eigenvalues and Eigenvectors
15. Notes on the Power Method and Related Methods
16. Notes on the QR Algorithm and other Dense Eigensolvers
17. Notes on the Method of Relatively Robust Representations (MRRR)
18. Notes on Computing the SVD of a Matrix
What You Will Learn in Linear Algebra: Foundations to Frontiers
"Linear Algebra: Foundations to Frontiers" by "M. E. Myers" and "P. M. van de Geijn" is a modern textbook designed to build a deep and structured understanding of linear algebra from the ground up. The book begins with the core ideas of vectors, matrices, and systems of linear equations, carefully guiding readers toward abstract thinking while maintaining clarity and logical flow.
A distinctive strength of this book is its balance between "theoretical foundations" and "computational insight". Rather than treating linear algebra as a collection of formulas, it emphasizes "algorithmic reasoning", matrix operations, and how mathematical structures support real computational tasks. Topics such as vector spaces, linear transformations, and eigenvalue problems are developed with precision and purpose, helping readers connect theory with practice.
Written for students in mathematics, engineering, computer science, and data-driven fields, the book supports active learning through well-organized explanations and progressive difficulty. Its approach encourages readers to think critically about "linear systems", understand "matrix factorizations", and appreciate the role of linear algebra in modern scientific computing. Overall, "Linear Algebra: Foundations to Frontiers" serves as a strong academic resource that bridges classroom theory and real-world application.
Book Details & Specifications
Title:
Linear Algebra: Foundations to Frontiers by M.E. Myers
Publisher:
ulaff.net
Year:
2014
Pages:
905
Type:
PDF
Language:
English
ISBN-10 #:
1292351217
ISBN-13 #:
978-1292351216
License:
External Educational Resource
Amazon:
Amazon
About the Author: Robert van de Geijnand and Maggie Myers
The author Robert van de Geijnand and Maggie Myers
are the authors of "Linear Algebra: Foundations to Frontiers", a modern textbook designed to connect theory with real-world computation. Myers focuses on "clear pedagogy", student-centered explanations, and helping learners build strong intuition in linear algebra concepts. Van de Geijn is a leading researcher in "numerical linear algebra" and "high-performance computing", widely known for the FLAME methodology for algorithm design. Together, they combine "education", "algorithms", "computation", "mathematical rigor", and "practical applications", making their work valuable for both students and professionals.
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