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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Review: Linear Algebra and Its Applications
User Review  Rahul Shrestha  GoodreadsGood one, but confusing concepts on Gaussian Elimination. Good reference book, not for learners! Read full review
Good for Undergrads and those who try to start from basics
User Review  Dinesh Dileep  FlipkartThe book is really nice if you are not exposed to linear algebra before. It patiently takes the reader through each concepts. Good if you are not familiar with linear algebra. If you do have a mathematical background, I would suggest Carl D Meyer's Matrix Analysis. Read full review