Lankham I. Linear Algebra As An Introduction to Abstract Mathematics 2016

Textbook in PDF format

This book aims to bridge the gap between the mainly computation-oriented lower division undergraduate classes and the abstract mathematics encountered in more advanced mathematics courses. The goal of this book is threefold:
You will learn Linear Algebra, which is one of the most widely used mathematical theories around. Linear Algebra finds applications in virtually every area of mathematics, including multivariate calculus, differential equations, and probability theory. It is also widely applied in fields like physics, chemistry, economics, psychology, and engineering. You are even relying on methods from Linear Algebra every time you use an internet search like Google, the Global Positioning System (GPS), or a cellphone.
You will acquire computational skills to solve linear systems of equations, perform operations on matrices, calculate eigenvalues, and find determinants of matrices.
In the setting of Linear Algebra, you will be introduced to abstraction. As the theory of Linear Algebra is developed, you will learn how to make and use definitions and how to write proofs. The exercises for each Chapter are divided into more computation-oriented exercises and exercises that focus on proof-writing.
Lecture Notes for MAT67 University of California, Davis written Fall 2007, last updated November 15, 2016