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What are some good sources for linear algebra for convex optimization and graph analysis? In Particular, is Gilbert Strang's MIT course suitable, or some other online course? I prefer online courses (video or lecture notes) to books because they're usually much better organized.

I'm at the undergrad level, but interested in doing research in machine learning and network theory, which use these two things respectively. I've taken one (basic, computationally-oriented: i.e. we didn't learn anything about basis, vector space or the meanings of linear mappings, but instead learned a lot about iterative methods Householder reflections) course on linear algebra, and all the time I find myself stymied by matrix formulations of optimization problems and assertions about eigenvalues of graphs.

I want to become fluent in it for these purposes - I don't plan to go further in the pure math direction, just engineering, so keep that in mind (though a few proofs and abstractions won't kill me, and are indeed welcome.

Side Question: Can you have a useful matrix of quaternions (since you can have complex as well as real matrices) or is that just a silly idea, for whatever reason?

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There is no problem with matrices whose entries are quaternions and these can be useful. You add and multiply in the usual way. You do encounter problems when it comes to the determinant and inverses because quaternion multiplication is not commutative. –  Bruce Westbury Jul 11 '10 at 12:18
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You might want to try looking at on-line linear programming courses. I suspect quite a few of these only assume the basics of linear algebra, and teach all the more advanced stuff that they use. These courses will include most of the material needed for convex optimization (although unfortunately not most of the material needed for eigenvalues of graphs). And don't worry too much about being stymied by matrix formulation of optimization problems -- even if you have had a good linear algebra course, you need quite a bit of practice to become fluent in these. –  Peter Shor Jul 11 '10 at 19:54
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I'll add that if you find you don't have enough background for a linear programming course, you should go ahead looking at a linear algebra course, and Gil Strang's is a fine one for this purpose. –  Peter Shor Jul 11 '10 at 19:58
    
Alright. I probably can learn something from a few of the Strang lectures (and I also have his book), but for now I'll focus on optimization. As far as graphs, I've found a few sources for that, but I'll probably be doing more paper-reading than anything else (I have next to me Lovasz's survey on Random Walks on Graphs). Thanks! –  DoubleJay Jul 12 '10 at 4:29
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