Linear Algebra and Its ApplicationsRenowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics. 
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I learned linear algebra with this book about 17 years ago. This book is great to study by yourself.
I just read this book three times and got A at the class.
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very good.
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References to this book
Nonnegative Matrices in the Mathematical Sciences Abraham Berman,Robert J. Plemmons No preview available  1994 