What is your best second books for linear algebra?

[Ask4material]

Hi, Everyone

It is difficult to find nice workable books for more advanced linear algebra.
There are numerous publications and internet materials, few of them are workable to me.

Interested topics:
unitary and Hermitian matrices, Jordan (canonical) form, tridiagonal matrix, Sylvester equation, Fibonacci det, factorizing, tensors, the QR form, spectral theorem, periodic matrix... etc, + some numerical methods and applications

Separated book recommendations for these topics are also welcomed.

Regards

 

[SolsticeFire]

When doing Lin Alg I used:

1) Linear Algebra Done Right - Sheldon Axler
2) Matrix Analysis - Carl D Meyer

I think most of the topics you listed can be found in Meyer's book; but if you want to really understand the crux of Linear Algebra, start with Axler and be patient.

SolsticeFire

 

[jasonRF]

What was the level of your first exposure to linear algebra?

If it was elementary (level of Anton, say) then for numerical linear algebra I recommend "fundamentals of matrix computations" by Watkins - cheap used copies of old editions would work. The 2nd edition is significantly better than 1st as it has added important material, but I have the 1st and found it great to learn from. Note you will also learn some more theoretical aspects of linear algebra along the way (invariant subspaces, etc.) as it is unavoidable - the nice thing is that you will see an immediate application!

If your background is higher level (Friedberg Insel and Spence, or Axler, ...) then I still like Watkins as a first introduction, but you may prefer the higher level books "applied numerical linear algebra" by Demmel or "numerical linear algebra" by Trefethen and Bau. Golub and Van Loan is the standard "bible" and could also be used - I find it to be great as a reference but a little too comprehensive (if that makes sense) to systematically work through.

best of luck,

jason