Table of Contents

Basic Notation and Terminology.- I. Fields and Integral Domains.- II. Vector Spaces.- III. Linear Independence and Dimension.- IV. Linear Transformations.- V. Endomorphism Rings of Vector Spaces.- VI. Representation of Linear Transformations by Matrices.- VII. Rings of Square Matrices.- VIII. Systems of Linear Equations.- IX. Determinants.- X. Eigenvectors and Eigenvalues.- XI. The Jordan Canonical Form.- XII. The Dual Space.- XIII. Inner Product Spaces.- XIV. Endomorphisms of Inner Product Spaces.- XV. The Moore-Penrose Pseudoinverse.- XVI. Bilinear transformations and forms.- XVII. Algebras over a field.