Linear Algebra is an important part of pure mathematics, and is needed for applications in every part of mathematics, natural science and economics. However, the applications are not so obvious as those of calculus. Therefore, one must study Linear Algebra as pure mathematics, even if one is only interested in applications. Most students find the subject difficult because it is abstract. Many texts try to avoid the difficulty by emphasizing calculations and suppressing the mathematical content of the subject. This text proceeds from the view that it is best to present the difficulties honestly, but as concisely and simply as possible. Although the text is shorter than others, all the material of a semester course is included. In addition, there are sections on least squares approximation and factor analysis; and a final chapter presents the matrix factorings that are used in Numerical Analysis.

Linear Algebra is an important part of pure mathematics, and is needed for applications in every part of mathematics, natural science and economics. However, the applications are not so obvious as those of calculus. Therefore, one must study Linear Algebra as pure mathematics, even if one is only interested in applications. Most students find the subject difficult because it is abstract. Many texts try to avoid the difficulty by emphasizing calculations and suppressing the mathematical content of the subject. This text proceeds from the view that it is best to present the difficulties honestly, but as concisely and simply as possible. Although the text is shorter than others, all the material of a semester course is included. In addition, there are sections on least squares approximation and factor analysis; and a final chapter presents the matrix factorings that are used in Numerical Analysis.