A First Course in Linear Algebra
by Robert A. Beezer
Publisher: University of Puget Sound 2010
Number of pages: 1035
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.
Home page url
Download or read it online for free here:
The book was designed specifically for students who had not previously been exposed to mathematics as mathematicians view it. That is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions.
by Andrew Baker - University of Glasgow
The text covers basic ideas and techniques of Linear Algebra that are applicable in many subjects including the physical and chemical sciences, and statistics. These notes were originally written for a course at the University of Glasgow.
by Ruslan Sharipov - Samizdat Press
This is a textbook of multidimensional geometry and linear algebra for the first year students. It covers linear vector spaces and linear mappings, linear operators, dual space, bilinear and quadratic forms, Euclidean spaces, Affine spaces.
by Peter Saveliev - Intelligent Perception
This is a textbook for a one-semester course in linear algebra and vector spaces. An emphasis is made on the coordinate free analysis. The course mimics in some ways a modern algebra course. Calculus is a prerequisite for the course.