Concise Introduction to Linear Algebra deals with the subject of linear algebra, covering vectors and linear systems, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors, singular value decomposition. It adopts an efficient approach to lead students from vectors, matrices quickly into more advanced topics including, LU decomposition, orthogonal decomposition, Least squares solutions, Gram-Schmidt process, eigenvalues and eigenvectors, diagonalizability, spectral decomposition, positive definite matrix, quadratic forms, singular value decompositions and principal component analysis. This book is designed for onesemester teaching to undergraduate students.

chapter 1|14 pages

Vectors and linear systems

chapter 2|29 pages

Solving linear systems

chapter 3|26 pages

Vector spaces

chapter 4|29 pages


chapter 5|17 pages


chapter 6|35 pages

Eigenvalues and eigenvectors

chapter 7|13 pages

Singular value decomposition

chapter 8|31 pages

Linear transformations

chapter 9|17 pages

Linear programming