Can someone explain what the Hadamard product is used for in math? It's definied for two vectors as z_i = x_i * y_i, and I believe it's also sometimes called the "vector multiply" (Golub and van Loan) or the "componentwise product," and I think it's denoted in TeX by x \circ y or something like that (I don't really know TeX).
Basically, I'm looking for a description of what is calculates, in the same way that I can say the dot product calculates the cos(angle) between vectors, etc.
I found a bunch of references to it on the web, but never a description of what it's actually doing with the input vectors. It's mentioned in Golub and van Loan's Matrix Computations at the beginning, but I don't know if it's mentioned again, and G&vL is at work and I keep forgetting to look when I'm at work and it's driving me nuts as I sit here at home. :)