Tracy Harms wrote:
> The composition on the right hand side is on linear maps
> (derivatives).
Representations of linear maps come from choosing bases, thereby
giving coordinates. If we do that, it's reasonably straightforward
except that we are misled by the 1-dimensional case.
Here's a simple 2-dimensional case.
g(x,y) = (x^2,y^2)
f(x,y) = (x^2+y,y)
(f @ g)(x,y)=(x^4+y^2,y^2)
D(f @ g)(x,y)= [4x^3 2y]
[0 2y]
Df(g(x,y)) Dg(x,y) = [2x^2 1][2x 0 ] = [4x^3 2y]
[1 1][0 2y] [0 2y]
Best wishes,
John
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