Preface This is a textbook for a two-semester course on Linear Algebra. Although the pre-requisites for this book are a semester of multivariable calculus, in reality everything is developed from scratch and …

This textbook is meant to be a mathematically complete and rigorous in-troduction to abstract linear algebra for undergraduates, possibly even first year students, specializing in mathematics.

This book begins with the central problem of linear algebra: solving linear equations. The most important ease, and the simplest, is when the number of unknowns equals the number of equations.

The notes are designed to be used in conjunction with a set of online homework exercises which help the students read the lecture notes and learn basic linear algebra skills.

This book starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on …

ThisbookhelpsstudentstomasterthematerialofastandardUSundergraduate firstcourseinLinearAlgebra. ThematerialisstandardinthatthesubjectscoveredareGaussianreduction, vector spaces, linear maps, …

a solution to the two equations. In linear algebra, we often are concerned with finding the solution(s) to a system of eq ations, if such solutions exist. First, we consider graphical representations of solutions …