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.

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 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.

This book usually develops linear algebra simultaneously for real and complex vector spaces by letting denote either the real or the complex numbers. If you and your students prefer to think of as an …

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

It provides the student with some picture of the origins of linear algebra and with the computational technique necessary to under­ stand examples of the more abstract ideas occurring in the later chapters.

Corollary. A linear system of n equations in n unknowns with matrix A has solutions for all augmented matrices if, and only if, the only solution of the corresponding homogeneous system is the trivial …

Linear Algebra Problems in Lemma My friend Pavel Grinfeld at Drexel has sent me a collection of interesting problems --mostly elementary but each one with a small twist.

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 …