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I have no problem understanding the basics of the linear algebra, but I also know that the linear algebra it's still an analytical approach to real world scenarios that can be solved with matrices and vectors.

Since I'm studying linear algebra exclusively because of virtual 3D world applications, I was wondering if there is a resource that can really help me to figure out what a certain operation on a matrix means or what is the real application of a particular property for a vector.

For example I know that if a given square matrix has all zeros in a diagonal ( Conference matrix ), I can assume that, if that matrix is being applied to an euclidean space in the 3D world to a 3D object, that 3D object is aligned with the main axis.

In other words I'm looking for a book that keeps an analytical approach based on mathematical properties and offers practical geometrical applications for them.

Since the main and hardest part it's about matrices, I can also accept books only about matrices, the important thing is keeping it practical about geometries and euclidean 3D.

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Try this out:

Some matrices include rotation, translation, shearing.

For virtual 3D world applications, you should look at computer graphics textbooks, like Computer Graphics with OpenGL by Hearn and Baker. This book discusses in detail the transformation matrices to move vertices around, and how to project onto the computer screen, project an object's shadow onto the ground using matrices. Fun stuff!

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thanks, you mean this one… ? – user2128456 Mar 11 '13 at 8:58
Yeah! If you are into programming, it is even better, since you can play around with matrix transformations and see how they affect your object. If not, there is still a nice discussion on using matrices for transformations, and composition of matrices to create complicated scenes. It is focused on computer graphics though, so it has other topics that don't use linear algebra. – user1526710 Mar 11 '13 at 16:28

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