I'm a graduate student studying quantum mechanics/quantum information and would like to consolidate my understanding of linear algebra. What are some good math books for that purpose?
Alvin Parks
Answered question
2022-11-21
Answer & Explanation
Aliya Moore
Beginner2022-11-22Added 17 answers
My favorite general book on linear algebra is Linear Algebra: An Introduction by Charles Curtis. This book is not only eminently readable, it's a book that balances theory and applications better then just about any book out there. It covers not only all the basics-linear spaces, linear independence, span,etc.-it also covers many sophisticated topics that aren't usually covered in basic courses and which are really important for further study, such as multilinear algebra and dual spaces. For a general text, this one can be matched,but not beaten.
However, there's a book I think you really need to look at after that given your area of interest and focus. That's Peter Lax's Linear Algebra And It's Applications . Not only is it beautifully written for a second course on linear spaces and it's written by one of the greatest living mathematicians there is-the book was specifically designed to act as a precursor to a graduate course on functional analysis. As a result, it focuses more on the analytical aspects of linear algebra then the algebraic or geometric aspects. To that end,Lax focuses much more on spectral theory and matrix analysis then other texts do.For example,chapter 10 contains a rapid but very complete introduction to the inequalities of matrix analysis.It's a wonderful read and will prepare you wonderfully for not only functional analysis, but the use of linear algebra and matrices in quantum theory.
Of course, after that, you should go directly to study Lax's beautiful text on functional analysis-which contains a number of applications to quantum theory, such as scattering theory.
New Questions in High school statistics
Read carefully and choose only one option
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