Preface. 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. Index.