Assuming one wishes to study numerical linear algebra in depth (and follow journals on numerical linear algebra and matrix theory), which would be a better course/better book to take up at first:
With Hoffman and Kunze with proofs and rigor (I don't have problems with rigorous math).
With Prof. Strang's book with un-rigorous proofs or "stated without proof" approach but heavy on applications and "real world" problems.
Any other you would recommend? (How about Gene Golub's book?)
I know some bits and parts of Strang's book (supplemented by his online lectures) and some portions of numerical linear algebra from Trefethen and Bau. But, I wish to have a more thorough understanding of the subject. I will mostly self-study the books.