Proof of a common f (x) = x 'A' ax derivative when the maximum value is obtained by using the Laplace method for PCA and least square difference

InPCAIn other places, when solving extreme values, we always encounterX 'A' axFunction pairXI have always seen the results given by others. Today I have deduced the results carefully. Here I will record this process.

The following is a proof of the use of the scalar formula to evaluate the column vector in the Process of proof. I will give it here:

Proof:

By the formula(1)You can get:

Certificate completed!

 

In fact, it is not difficult to prove it by definition. it is difficult not to regard the transpose of X as an X composite function. In this way, the derivation formula of this composite function cannot be found. You can find a way to convert the vector evaluation to a number, and then apply the evaluation formula.