Two things:

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

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 [tex] \mathbb{R}^{n^2} [/tex] I am asked to prove that [tex] df_{A_0} (X) = -X [/tex] where [tex] A_0 [/tex] is the identity matrix. My question is, [tex] df_{A_0} [/tex] would usually denote that derivative of f at the point [tex] A_0 [/tex], so where does that (X) part come into play?

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.

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

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 [tex] \mathbb{R}^{n^2} [/tex] I am asked to prove that [tex] df_{A_0} (X) = -X [/tex] where [tex] A_0 [/tex] is the identity matrix. My question is, [tex] df_{A_0} [/tex] would usually denote that derivative of f at the point [tex] A_0 [/tex], so where does that (X) part come into play?

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.

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