Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques.
The book is intended to be used in one of several possible ways:
(1) as a self-study guide;
(2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or
(3) as a reference book.
It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams.
The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
The book is intended to be used in one of several possible ways:
(1) as a self-study guide;
(2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or
(3) as a reference book.
It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams.
The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication. The book also contains over 1000 exercises, many of which are very challenging.
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)
"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)