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.
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2Cf. Hadamard product; cf. this question – J. W. Tanner Apr 02 '21 at 01:43
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The main reason this isn’t much discussed is that it isn’t so much a vector operation as it is a “block” operation. Vectors are not rows of numbers, they are geometric objects. – Thomas Andrews Apr 02 '21 at 01:51
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This is also called “component-wise multiplication” or “slot-wise multiplication” but Hadamard product is the formal name. – mweiss Apr 02 '21 at 13:03