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Where to begin? I'd pick a problem that is easy, but not trivial, and work it out in Mathematica. After a couple of such exercises, you'll be ready to use it in your real work. Since you mention linear algebra, how about something that gets you using EigenSystem or SingularValueDecomposition? Or maybe you have something you'd like to plot? There are great ...

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I found this book to be extremely useful in learning advanced functionalities in Mathematica: "Mathematica Cookbook" of Sal Mangano http://shop.oreilly.com/product/9780596521004.do It has many examples of matrices and plots uses and several tips from other topics and uses that go beyond the documentation's. Hope it helps

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If you are relatively new to Mathematica, I would definitely pick up a copy of "Programming with Mathematica: An Introduction" by Paul Wellin. This will give you an excellent starting point and solid foundation before you progress to more advanced material. I am still working my way through Paul's book, but it has been well worth it and has really opened my ...

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The references mentioned in the other answer do not really pertain too much to the problem of minimax approximation; they are more concerned with the other functions in FunctionApproximations that deal with numerical differential equation solving; that is, the content that was once in the old NumericalMathpackages Butcher and OrderStar. Indeed, a look ...

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