The techniques of linear algebra are used extensively across the applied sciences, and in many different areas of algebra such as group theory, module theory, representation theory, ring theory, and Galois theory. Written by experienced researchers with a decades of teaching experience, Introduction to Linear Algebra is a clear and rigorous introductory text on this key topic for students of both applied sciences and pure mathematics.

chapter 1|9 pages

Linear Vector Spaces

chapter 2|11 pages


chapter 3|7 pages


chapter 4|11 pages

Invertible Matrices

chapter 5|8 pages

Linear Systems

chapter 6|9 pages

Linear Systems

chapter 7|6 pages


chapter 8|8 pages

Linear Dependence and Independence

chapter 9|7 pages

Bases and Dimension

chapter 10|6 pages

Coordinates and Isomorphisms

chapter 11|7 pages

Rank of a Matrix

chapter 12|9 pages

Linear Mappings

chapter 13|7 pages

Matrix Representation

chapter 14|11 pages

Inner Products and Orthogonality

chapter 15|7 pages

Linear Functionals

chapter 16|10 pages

Eigenvalues and Eigenvectors

chapter 17|9 pages

Normed Linear Spaces

chapter 18|10 pages


chapter 19|6 pages

Singular Value Decomposition

chapter 20|11 pages

Differential and Difference Systems

chapter 21|6 pages

Least Squares Approximation

chapter 22|7 pages

Quadratic Forms

chapter 23|8 pages

Positive Definite Matrices

chapter 24|7 pages

Moore–Penrose Inverse

chapter 25|11 pages

Special Matrices