Let

be continuously differentiable functions and suppose there is a diffeomorphism

on

such that:

for any

where

is the Jacobian of

at

Obviously,

is a zero of

iff

is a zero of

.

Show that in this case, the Jacobian of

at

and the Jacobian of

at

are similar

matrices.

-------------

When

, this is easy because the Jacobian is just the regular derivative and I can apply the quotient rule.

(Of course, two

matrices are similar only when they are equal)

But how can I handle the general case? Even when

, the calculations get quite tedious to do by hand.

Thanks a lot