what is the name of a regular (column * column) product of a vector

Question

Let $A = |a_{0},a_{1}, a_{2},... a_{n} |$ and $B = |b_{0},b_{1}, b_{2},... b_{n}|$. If we define a vector function $product$ such that $product(A,B)=|(a_{0}b_{0}) , (a_{1}b_{1}) , (a_{2}b_{2}),\dots, (a_{n}b_{n}) |$, is there a standard name for a vector operation that is equivalent to $product(A,B)$? In more simple words, has noone thought of defining an operation for a simple product between column values of a vector (what I like to call the excel product, hahaha), but there has been defined operations for things related to angles of vectors as products? I searched a lot and didn't find anything about this.

Answer 1

Your product is a special case of the Hadamard product of matrices.