How can I determine the linear part of f(A + H) in terms of H?

[Maybe_Memorie]

Homework Statement

Let f:R^nxn-->R^nxn be defined by f(A) = A². Prove that f is differentiable. Find the derivative of f.

Homework Equations

f(a + h) = f(a) + f'(a)h + \phi(h)

The Attempt at a Solution

f(A + H) = (A + H)² = A² + AH + HA + H²

f(A) is given by A². So the sum of the derivative operator and the remainder term is AH + HA + H². The problem is that I don't know how to determine which terms are part of the derivative.

 

[Office_Shredder]

The derivative is the linear part of AH+HA+H² in H. So the question is which part is linear and which part is not?