# Linear Algebra for QM

I just finished a course on linear algebra. The class was quite slow, and not much material was covered (essentially going as far as diagonalization w/ some applications). Seeing as I will be taking a QM course next semester, I thought that it might be a good idea to advance myself on the math behind QM over the summer. Could someone recommend a suitable advanced linear algebra text that would be appropriate for QM?

I just finished a course on linear algebra. The class was quite slow, and not much material was covered (essentially going as far as diagonalization w/ some applications). Seeing as I will be taking a QM course next semester, I thought that it might be a good idea to advance myself on the math behind QM over the summer. Could someone recommend a suitable advanced linear algebra text that would be appropriate for QM?

Try the first chapter of "Principles of Quantum Mechanics - R. Shankar" called Mathematical introduction,and you will know exactly what you are going to learn

Fredrik
Staff Emeritus
Gold Member
I think Axler is excellent for QM. You should stay away from books that delay the introduction of linear transformations/operators instead of introducing them early. For example, Anton defines them around page 300, which is just ridiculous. Make sure you understand the relationship between linear operators and matrices (i.e. this) perfectly.

Try the first chapter of "Principles of Quantum Mechanics - R. Shankar" called Mathematical introduction,and you will know exactly what you are going to learn
I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?

I think Axler is excellent for QM. You should stay away from books that delay the introduction of linear transformations/operators instead of introducing them early. For example, Anton defines them around page 300, which is just ridiculous. Make sure you understand the relationship between linear operators and matrices (i.e. this) perfectly.
That stuff I know already. My linear prof had promised, in the beginning of the course, to discuss infinite-dimensional vector spaces, as well as certain types of matrices and their properties (ie hermitean, adjoint, etc.)

I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?

The book by https://www.amazon.com/dp/0486453278/?tag=pfamazon01-20 may be what you're looking for. At least you'll find links to many similar books on that page.

You could also try a math methods book like https://www.amazon.com/dp/048667164X/?tag=pfamazon01-20.

Or the many books aimed at https://www.amazon.com/s/ref=nb_sb_...chanics+for+mathematicians"&tag=pfamazon01-20.

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I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?

That stuff I know already. My linear prof had promised, in the beginning of the course, to discuss infinite-dimensional vector spaces, as well as certain types of matrices and their properties (ie hermitean, adjoint, etc.)

So try Dirac's book...I think in QM you will ned most Kets and Bras Algabra

A. Neumaier
I skimmed through it, and although it seems good, I'm always a little suspect of physics texts that try to teach math. My experience is that they are generally rushed, and important ideas and concepts are missed in the process. Would you happen to know a book exclusively dedicated to the same topics, but more thorough?

Try http://de.arxiv.org/abs/0810.1019