Recommend a self study book for linear algebra with complex numbers
I saw that you needed this for QM. In that case, everything you need to know is in this beautiful and excellent book: http://www.math.brown.edu/~treil/papers/LADW/LADW.html
You will find that LA over complex numbers is not very different from LA over the reals. But you'll see many topics in this book that are helpful for QM.