Kuttler K. A First Course in Linear Algebra 2014

Textbook in PDF format

The book presents an introduction to the fascinating subject of linear algebra. As the title suggests, this text is designed as a first course in linear algebra for students who have a reasonable understanding of basic algebra. Major topics of linear algebra are presented in detail, with proofs of important theorems provided.
This text intends to transform students from passive observers of mathematics to participants in it. The book employs a spiral development of ideas to blend the requirements of problem solving, analytical thinking, computational technique, and applications, and emphasizes the interplay of algebraic and geometric concepts. It includes an extensive number of exercises, ranging from routine to challenging
Systems of Equations
Matrices
Determinants
Rn
Linear Transformations
Complex Numbers
Spectral Theory
Some Curvilinear Coordinate Systems
Vector Spaces
Some Prerequisite Topics
Selected Exercise Answers