Linear Algebra: A Modern IntroductionDavid Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlying geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra. 
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This "book" is an absolute trainwreck. It takes a completely abitrary trip through the subjects of linear algebra without any clear buildup whatsoever. Half the critical concepts of a paragraph are put into "examples" and "theorems", which make it absolutely horrendous if you just want to look up one thing.
To understand how to write a line using a single interpretation (i.e. write a vector normal form), prepare to read 34 pages in paragraph 1.3 where 90% of the text is irrelevant to the subject explained.
They claim to establish a link between algebraic notation and "geometric intuiition", which is a plain lie. Nowhere in the book does it even attempt to translate ideas from an algebraic to a geometric viewpoint.
Worst math book I have ever had. Some practice questions have no relevant examples, solutions use notation not even mentioned in that section of the text. Don't even try to get the correct process and notation without paying an additional 7580 dollars for the solutions manual. All in all a terrible, extremely overpriced resource for those unfamiliar with the subject. Poole forgets what it is like to not be a trained mathematician who is just learning the subject.