Numerical Linear AlgebraThis is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization  an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra. 
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This is an excellent book on numerical linear algebra, a very good textbook for a senior undergraduate course. I like the writing style and have been enjoying the reading. Very often it explains "why", not just gives "what" and "how". Highly recommended.
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The strength of this book is in the conceptual discussions. This isn't the book to use to learn the mechanics of the methods described. It's one of my three favorite numerical linear algebra books.