Linear Algebra Book satisfying those reqs

Long before, I studied strang's linear algebra book with MIT video lectures. It was good and well designed course which I liked, but it is a bit prescriptive and I am having difficulties with LA.

I read books on computer graphics, vision, machine learning and will read books on convex optimization linear dynamical systems etc. which both apply and use theory of LA.

But I am having difficulties truly understanding these concepts with my LA level. So I need a book strong at theory and geometric intuition of LA. I know how can I find eigen vector but I am not sure what exactly it does, I don't exactly know what affine transform is, and never exposed to rigoruous definition of vector space all I know is orthogonal bases and projection, basis changing etc..

The books I plan to read are hoffman kunze and after that axler's LA done right.

Are these the books which I need or do you recommend ones which are good for above mentioned needs ?

I am currently reading baby rudin so I am mostly okey with proofs.

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Does these work? You can see the TOC and sample pages on sites like Amazon to see if it meets your needs.

1. Linear Algebra Through Geometry (Undergraduate Texts in Mathematics) [Hardcover], Thomas Banchoff (Author), John Wermer (Author)

2. Linear and Geometric Algebra [Paperback], Alan Macdonald (Author)

You may also want to review this previous response: http://mathoverflow.net/questions/16994/linear-algebra-texts

Maybe you can go through this open course-ware series at MIT (there are other examples like this too): http://www.catonmat.net/blog/mit-linear-algebra-part-one/

Regards -A

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I did MIT stuff it is not what I look. I am loking for a LA out of matrix theory. I am good up to SVD but problem is why such a decomp work what the hell matrix is decomposed so ? from space ? why ? – camoka Dec 4 '12 at 1:16
Great resources! $\large + 1 \land \checkmark$ – amWhy May 17 '13 at 0:36

This one is free online or you can give a donation First Course in Linear Algebra by Robert A. Beezer Department of Mathematics and Computer Science University of Puget Sound.

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Try also Practical Linear Algebra: A Geometry Toolbox, which is concrete and has nice pictures.

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