Colloquium Publications 1934; 205 pp; softcover Volume: 17 ISBN10: 0821846108 ISBN13: 9780821846100 List Price: US$50 Member Price: US$40 Order Code: COLL/17
 It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of resultsthe subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. Jahrbuch über die Fortschritte der Mathematik In 1937, the theory of matrices was seventyfive years old. However, many results had only recently evolved from special cases to true general theorems. With the publication of his Colloquium Lectures, Wedderburn provided one of the first great syntheses of the subject. Much of the material in the early chapters is now familiar from textbooks on linear algebra. Wedderburn discusses topics such as vectors, bases, adjoints, eigenvalues and the characteristic polynomials, up to and including the properties of Hermitian and orthogonal matrices. Later chapters bring in special results on commuting families of matrices, functions of matricesincluding elements of the differential and integral calculus sometimes known as matrix analysis, and transformations of bilinear forms. The final chapter treats associative algebras, culminating with the wellknown WedderburnArtin theorem that simple algebras are necessarily isomorphic to matrix algebras. Wedderburn ends with an appendix of historical notes on the development of the theory of matrices, and a bibliography that emphasizes the history of the subject. Readership Graduate students and research mathematicians interested in matrices. Table of Contents  Matrices and vectors
 Algebraic operations with matrices. The characteristic equation
 Invariant factors and elementary divisors
 Vector polynomials. Singular matric polynomials
 Compound matrices
 Symmetric, skew, and hermitian matrices
 Commutative matrices
 Functions of matrices
 The automorphic transformation of a bilinear form
 Linear associative algebras
 Notes
 Bibliography
 Index to bibliography
 Index
