[Math] Life after linear algebra and multivariate calculus

calculuslinear algebrastatistics

I have been following Strang's Linear Algebra course, and found it quite challenging. My goal, however, is to learn application of linear algebra and calculus in applied statistics (regression, linear mixed models, structural equation modeling, et cetera). I want to understand the math behind these techniques. Some people suggest learning abstract algebra after linear algebra. However, after trying one to two lectures by Benedict Gross (on youtube), I find that it is totally not for me – I was lost very soon about what he talked about. In addition, I am unsure if abstract algebra is very useful to applied statistics. Therefore, I am unsure what I should learn after linear algebra and calculus, and I preferably want to learn something with online videos (as self-learning stats can be quite difficult).

Best Answer

One place in statistics where abstract algebra (specically finite fields) is used is in the construction of mutually orthogonal latin squares which are used in Design of (statistical) Experiments. Knowing linear algebra, matrix, eigenvalues, positive definiteness, generalized inverses is the most important thing. You can safely skip abstract algebra and focus on applications of matrices. One small book that does this well is by Bapat (Linear Algebra and Linear Models?) published by Hindustan Book Agency, New Delhi.

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