Any good sources on complex vector spaces?

I have two textbooks that work through undergraduate-level (for math majors) linear algebra in a very abstract, structure-orientated fashion, such that the nature of the field underlying the vector spaces matters very little in the development. The emphasis of these texts is understanding the category of vector spaces and linear transformations rather than drilling matrix computational techniques. That you would need a text focusing specifically on complex vector spaces (finite dimesional, right?) makes me think your courses are approaching the subject from the computational perspective. Am I correct?

And your professor can’t suggest one?

@hiphiphopflipflapflop My linear course actually focused much more on theory than on computations. I expect that my complex course will be even less computational since there are only math majors taking it (about half of the students in linear were engineering majors, which affected the nature of the course). My linear book was not particularly abstract, but my professor did not use it. He taught from his notes, which were virtually a book in themselves, and were primarily abstract.

Today, we were looking through the many linear books in his office, and none of them really had what we want. I can’t very well buy a bunch of books to see if they have what we’re looking for, so I figured I would ask if anyone already knows of one.

This might be something better suited to folks at Math Overflow.

@hiphiphopflipflapflop Thank you! I had never heard of that site. It looks interesting.

You’re welcome!

They’ll probably want a very explicit and detailed statement of the properties of the text you are seeking to keep the discussion focused rather than have it degenerate into “everybody mention your favorite linear algebra text here”.

Check here to see if Halmos’ classic Finite Dimensional Vector Spaces might work.