
In this book the authors present classical and recent results for matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematics, and the necessary material has only occurred sporadically in the literature and university curricula. As the interest in applied mathematics has grown, the need for a text and a reference work offering a broad selection of topics has become apparent, and this book aims to meet that need. This book will be welcomed as an undergraduate or graduate textbook for students studying matrix analysis. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. They begin with a review and discussion of eigenvalues and eigenvectors. The following chapters each treat a major topic in depth. This volume should be useful not only as a text, but also as a self-contained reference work to a variety of audiences in other scientific fields.
Matrix Analysis by Horn and Johnson (perhaps the best end-of-chapter problem sets of any math book I've encountered!)
Matrix Computations by Golub and Van Loan
Elements of Statistical Learning by Hastie, Friedman, Tibshirani
Functional Analysis by Reed and Simon
Hawking was great, and wrote a fantastic book called "God Invented the Integers" where he details fascinating seminal math contributions.
I'm a geek for Horn and Johnson of Matrix Analysis fame.
Munkres topology has been bedtime reading for a long time.
Quite a few philosophers strike my fancy, especially the existential school.