In Linear Algebra, when computing an inner product $
If it doesn't have a name, where can I find a practical explanation of how to construct it for a particular problem or space?
Is there a text on the subject that explains this simply? A note on my background, I am approaching this from the perspective of an engineering student and not that of a mathematician; I don't have an understanding of the finer points of topology or differential geometry (not yet at least :) ).
I believe that this is the same matrix used in vector calculus to perform a change of variables. As in, we perform our change of variables, then multiply the new expression by $\frac{det(J(W))}{det(J(V))}$ where $W$ is this magic matrix in the new space, $V$ is this magic matrix the old space, and J(X) is the Jacobian operator. Am I correct?
Also, is this related to one of the the matrices that comes up in Singular Value Decomposition (namely the diagonal matrix containing the singular values)?