Two things:

1) If we say that the space of all 2 by 2 matrices is identified with R^4, what does that mean?

Write both rows of a matrix one after the other with commas between the entries and enclosed in parentheses:

...this is an element of , and this is what is meant, since the other direction if also clearly true.
2) Suppose f is a function from GL(n, R) to GL(n, R) (the space of all real n by n invertible matrices) identified with

I am asked to prove that

where

is the identity matrix. My question is,

would usually denote that derivative of f at the point

, so where does that (X) part come into play?

I don't know this one, but I think the notation may denote directional derivative of in the direction of ...I can't say

Tonio
I know that I should be asking my prof this, but I wanna do these homework questions before my next class (Wednesday), so it would be great if you guys could help me out.