Remarks on Linear Algebra

We don't need to worry too much on linear algebra as the only fact that we use in the midterm and final exam is that for square matrix $A$, \[ A\text{ is invertible} \iff \det A\neq 0. \] We will need this fact when applying inverse function theorem and implicit function theorem. A better background in linear algebra arguably assists one in understanding each (rigorous) definition in multivariable calculus.

Some of you may want to review the whole subject thoroughly, here are some suggested texts:

1. Linear Algebra Done Right/線性代數是這樣學的 (which we learn without too much computation, especially determinant will be presented in the last chapter)
2. Algebra by Michael Artin (also helps a lots for students taking Algebra I)
3. Tutorial notes of linear algebra this semester of BEST TA:
   
   http://ihome.ust.hk/~kero/2121.html
4. My notes on linear algebra (which grow out of my too lengthy tutorial notes of Math2121)
   
   http://ihome.ust.hk/~cclee/document/MATH2121/Combine_Notes.pdf

In learning mathematics I usually read only a few books, and spend a lot of time on solving the problems (which I feel meaningful/fancy) in the exercises. So the above are all that I can suggest :).