This book begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. Material in this new edition has been rewritten and reorganized and new exercises have been added.
“The present textbook is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of finite-dimensional vector spaces and proceeds to explain the structure theorems for linear maps, including eigenvectors and eigenvalues, quadratic and Hermitian forms, diagonalization of symmetric, Hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. It also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps. “
About the Author
Serge Lang was born in Saint-Germain-en-Laye close to Paris. His father Étienne Lang was a businessman and his mother Helene Schlepianoff was a concert pianist. Serge had a twin brother who became a basketball coach and a sister who became an actress. Serge lived in Paris and attended school there until the beginning of World War II when he was in the 10th grade. The war began in September 1939 but it was not until June 1940 that German troops entered Paris. Serge together with his father and sister fled to the United States where they settled in Los Angeles, California. It was there that Lang completed his high school education and then entered the California Institute of Technology.
Lang graduated from the California Institute of Technology in 1946 with a B.A. in physics. He then served for around eighteen months in the U.S. Army and he was stationed for part of this time in Italy and Germany. After returning to the United States, Lang went to Princeton University with the intention of studying for a doctorate in philosophy. After a year in the philosophy department, he changed to mathematics and Emil Artin became his thesis advisor. He was awarded his Ph.D. in 1951 for his dissertation On Quasi Algebraic Closure.
Solutions Manual of Lang’s Linear Algebra | 1st edition ISBN 9780387947600
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Solutions Manual of Lang’s Linear Algebra