Re: ? N eqns and N unknowns

Cheng Cosine wrote:
Hi:

What is the name of the theorem that says that

one must have N linearly independent equations to

solve for N unknowns?


I don't know if it goes by any name. It's shown in linear algebra. But
see below.


The above is for linear equations, what if one has

N non-linear equations for N unknowns?


Then the Inverse Function Theorem provides a generalization of the above
situation for a system of n linear equations in n unknowns. The theorem
gives you local existence of a unique solution provided the
linearization of your system at a particular point is nonsingular.

Have a look at

http://planetmath.org/encyclopedia/InverseFunctionTheorem.html

Thanks,
by Cheng Cosine
Oct/20/2k6 NC




.

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