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This is my first post, so I do apologize if I’ve missed something important.

I’m preparing to pursue a PhD in statistics, and I’ve recently realized that my linear algebra knowledge is not “up to par.”

The class that I took only stopped at orthogonal sub spaces, and I know that’s just not sufficient.

Does anyone have any recommendations for a linear algebra textbook that would be sufficient for self study and get me to the level that I need?

I’ve heard some, good things about Linear Algebra Done Right and Linear Algebra Done Wrong.

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Hello Statistijed and welcome to Cross Validated! I am sure you will get a lot of different answers on here but my recommendation (given that you have a good grasp of everything in a basic undergrad linear algebra course (so I would say through Axler Ch.3 at least)) is to focus on "Numerical Linear Algebra" and "Matrix Computations". I find this computational approach to linear algebra to be more useful, atleast that has been the case for me so far.

So I'd recommend picking up either Watkins or Golub and Van Loan and working through whatever seems most interesting. At the very least make sure you get SVD in and maybe also LU factorization. The least squares problems might also be interesting to you.

This is just my opinion, of course. Good luck!

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Good sources for learning linear algebra for statistics is books about multiple linear regression of multivariate statistics with appendices detailing what they need. Look at Seber and Lee or Mardia, Kent & Bibby. Or more modern works like those listed at Looking for modern references in Mathematical Multivariate Statistics. Then you will also see what kind of linear algebra you need to understand!

A linear algebra introduction geared for statistics is Linear Algebra and Learning from Data, which looks rather interesting. This is an introduction structured around various tasks to do with data!

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These spring to mind :

Matrix algebra useful for statistics. Searle, S. R., & Khuri, A. I. (2017). John Wiley & Sons.

Linear Algebra and Matrix Analysis for Statistics Banerjee, S., & Roy, A. (2014). Crc Press.

Numerical linear algebra for applications in statistics. Gentle, J. E. (2012). Springer Science & Business Media.

Also, this is a classic, although not specific to statistics:
Introduction to linear algebra (Vol. 3) Strang, G.(1993). Wellesley, MA: Wellesley-Cambridge Press.

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Trefethen, Lloyd N., and David Bau III. Numerical linear algebra. SIAM, 1997

is comprehensive easy to read. A good portion of the book is available at the author's website.

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Can't recommend specific books, but what you need to get well-versed on is:

  • Some introduction to vector spaces.
  • Linear applications and its basic properties.
  • Diagonalization and Jordan forms of matrices.
  • Inner products, norms and Gram's matrices.

If you master these topics, there's not much linear algebra that will put you in trouble

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