Linear Algebra a Beginning Graduate Student Ought to Know

From the reviews of the third edition: "This edition is enhanced by the inclusion of further results and many new examples. There are also over 130 additional exercises and many of the earlier ones have been revised. Furthermore, many more biographical notes and thumbnail portraits of mathematicians connected in some way with linear algebra have been added. This book continues to be very successful and useful, not only as a textbook for advanced linear algebra courses, but also for self-study and reference purposes." (Rabe von Randow, Zentralblatt MATH, Vol. 1237, 2012)

• Notation and terminology.- Fields.- Vector spaces over a field.- Algebras over a field.- Linear independence and dimension.- Linear transformations.- The endomorphism algebra of a vector space.- Representation of linear transformations by matrices.- The algebra of square matrices.- Systems of linear equations.- Determinants.- Eigenvalues and eigenvectors.- Krylov subspaces.- The dual space.- Inner product spaces.- Orthogonality.- Selfadjoint Endomorphisms.- Unitary and Normal endomorphisms.-  Moore-Penrose pseudoinverses.- Bilinear transformations and forms.- Summary of Notation.-Index to thumbnail photos.