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The last time I have taken Linear algebra I was 4 years ago and it was very computational. Over the past year I have studied logic, predicate calculus, and symbolic logic. These topics renewed my interest in mathematics.

Determinants, matrices, and systems of linear equations; linear dependence; vector spaces; eigenvalues, and eigenvectors; matrix equations; linear transformations; convex sets. These are the topics that will be taught in the class but because of my gap I honestly don't even know where to begin. What exactly should I review to help me prepare for the class and what should I expect from this class?

Help would be appreciated thank you!

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closed as off-topic by Will Jagy, Claude Leibovici, Lord Shark the Unknown, mlc, Rafa Budría Jun 10 '17 at 8:45

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  • $\begingroup$ Read the textbook you'll be using ahead of time! They often have reasonable intro chapters, and if not you'll find specific topics to review from where you get stuck. $\endgroup$ – Artimis Fowl Jun 10 '17 at 0:44
  • $\begingroup$ I recommend reading Introduction to Linear Algebra by Strang. $\endgroup$ – littleO Jun 10 '17 at 0:44
  • $\begingroup$ As littleO suggested Linear algebra by Strang is a great book, but as someone who worked both in both pure and applied it is important what class and at which school you are taking. If your class is beginning pure math read "Linear Algebra Done Right", if it is more advanced .. well it depends what field do you concentrate at (algebra, geometry, etc..). If you are in the applied, I agree Linear Algebra by Strang is a great beginning. $\endgroup$ – Kori Jun 10 '17 at 1:05
  • $\begingroup$ Linear algebra has few if any prerequisites, so I agree with the advice to just start learning linear algebra with proofs ahead of time. As an alternative to Axler's book, which is also good, I would recommend Introduction to Linear Algebra by Serge Lang. If that turns out to be too difficult, there is always the option of reading a so-called "transition to higher mathematics" book. My favourite one of those is Journey into Mathematics by Rotman, which has a free solutions manual on the Dover website. Another possibility, if you find the recommended linear algebra books difficult, is $\endgroup$ – user49640 Jun 10 '17 at 2:51
  • $\begingroup$ to study vector geometry first. This is the use of vectors to solve various geometry problems concerning lines, planes, etc. This gives the geometric intuition that is so helpful in learning linear algebra. Lang's book has a bit of this in its first chapter, but a more complete treatment can be found, for instance, in Elementary Vector Algebra by Macbeath. But if this was part of what you learned four years ago, it won't be as useful, because it will come back to you without too much effort. $\endgroup$ – user49640 Jun 10 '17 at 2:54

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