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In summary, linear algebra is a subject that covers vector spaces, inner products, linear independence, orthonormal bases, linear operators, matrix multiplication, the relationship between linear operators and matrices, the adjoint operation, eigenvectors and eigenvalues.

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I should have mentioned determinants as well. If you understand these things, you're off to a good start. I've been told that Friedberg, Insel & Spence is a very nice book. Axler is also good. There are several other acceptable choices. I would however recommend that you stay away from books like Anton, which wait as long as possible with the introduction of linear operators (also called linear maps, linear functions or linear transformations). The sooner they are introduced, the better.Fredrik said:The concepts from linear algebra that you need to understand are: vector spaces, inner products, linear independence, orthonormal bases, linear operators, matrix multiplication, the relationship between linear operators and matrices, the adjoint operation, eigenvectors and eigenvalues.

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here are at least two free linear algebra books:

http://www.math.uga.edu/~roy/look for the free notes.

#1) is a 15 page linear algebra book covering everything in basic linear algebra excelt determinants.

#7) covers even that, and much more in more detail in less than 100 pages.

If you are picky and want a really good book, here is one 250 pages long by Sergei Treil:

http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf [Broken]

http://www.math.uga.edu/~roy/look for the free notes.

#1) is a 15 page linear algebra book covering everything in basic linear algebra excelt determinants.

#7) covers even that, and much more in more detail in less than 100 pages.

If you are picky and want a really good book, here is one 250 pages long by Sergei Treil:

http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf [Broken]

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bcrowell said:

Sorry to get off topic, but...

Thank you sooooo much! I've been trying to understand the concept of a vector space for the past week and a half. This has been the best explanation to me so far! Thanks!

Linear algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of matrices, vectors, and linear transformations.

The main topics covered in a linear algebra class include vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors, and systems of linear equations.

Linear algebra is important because it is used in many fields such as physics, engineering, computer science, and economics. It provides a powerful tool for solving complex problems and understanding real-world phenomena.

Linear algebra has numerous applications, including computer graphics, data analysis, machine learning, cryptography, and optimization. It is also used in physics to describe the behavior of physical systems.

Linear algebra can be challenging for some students because it introduces new concepts and requires a strong foundation in algebra. However, with practice and perseverance, it can be a rewarding and valuable subject to learn.

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