Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory [Book review; D.S. Berstein]

This text is the encyclopedic work on matrices that has been sought for more than 50 years. The bibliography alone contains 820 items. Of the approximately volume's 750 pages, some 190 are devoted to bibliography, indexing, and notation. The reader thus has an excellent chance to determine if the idea which is sought is to be found in this volume. Students will find that the book can be used to expand the scope of their course textbook. The one drawback is that only a portion of the results in the book appear together with a proof. Professors can use the text to supply exercises to augment standard material in matrix courses. Another possible usage is as a general reference for researchers in mathematics, statistics, physics, and engineering. The book could also be used by the reader to "peruse" and determine whether the reader knows as much as he thinks he does. While the lack of proofs may pose a problem, and some topics are not explored as well as one might hope, the book is a monumental contribution which takes a serious step toward "systematizing" an absolutely huge area of theory and application.