I am aware that there are plenty of questions regarding book recommendations, however, I have not found one that fully matches what I intend to ask. I have provided a list of links to some similar questions under my question.
I am 2nd year Undergrad doing physics. So far we have completed three "Mathematics for Scientisits" courses and they are all heavily based on matrices, vectors, orthogonality and linear algebra in general. However, the motivation behind the methods is not explained at all! All sorts of terminology is thrown around and I hit a brick wall when I try to connect it all together.
I can, for the most part, do the maths behind them but I am failing to fully grasp the pure and applied concepts of:
- Orthogonality
- Eigenvalues and Eigenfunctions
- Inner product, vector space
- (Essentially, the range of topics in Linear Algebra)
Mainly, I am curious as to why they are used so much in quantum mechanics. We have not been introduced to Hilbert Space yet (nor Dirac notation, which worries me); I think those things will be studied next year but might as well learn them now.
Having said all that, I am looking for books, both for mathematicians and/or physicists, which explain the meanings, concepts and uses of all this abstract mathematics well. It would be an added bonus if they have good practice questions too. I am looking for books that have thorough, well written explanations.
After doing a bit of research I am most intrigued by:
- Linear Algebra: Concepts and Methods by M. Anthony and M. Harvey
- Linear Algebra and Its Applications by David C. Lay
Any comments on those before I buy them?
List of links of related questions:
Best Books for Mathematical Background
Linear Algebra for Quantum Physics
