Jan 2, 2023 · The vector dot and cross product are not some kind of analogue or generalization of the arithmetical product's sense of repeated addition. (Indeed, I try to avoid using "multiply", since the …

Aug 31, 2019 · One motivation for these types of vector multiplication is that we can perform geometric calculations in three-dimensions through purely algebraic methods; for example, since the dot …

Feb 27, 2011 · There are several meaningful definitions of vector multiplications. Out of these, the inner product multiplication (or dot product) is most abundant in physics. We take force vectors and …

Wikipedia also mentions it in the article on Matrix Multiplication, with an alternate name as the Schur product. As for the significance of element-wise multiplications (in signal processing), we encounter …

Sep 15, 2015 · In Coding the Matrix, I define matrix-vector multiplication, which operates on a matrix and a vector. The number of columns of the matrix must match the number of entries of the vector.

Jul 20, 2011 · I recommend writing componentwise multiplication of vectors using some symbol that does not have a standard meaning, perhaps $\star$ (\star) or $\diamond$ (\diamond), so that people …

I was just wondering why we don't ever define multiplication of vectors as individual component multiplication. That is, why doesn't anybody ever define $\\langle a_1,b_1 \\rangle \\cdot \\langle a_2,...

Aug 3, 2016 · If you want to implement these algorithms, you should read related papers and work on some examples with Kronecker products of three matrices. Introduction Shuffle algorithm (Plateau, …

Dec 15, 2017 · You can invent your own product or way of multiplication, but the standard product of matrices only works, as you say, when the number of columns of the first matrix matches the number …

Jul 22, 2015 · Scalar Multiplication Example: $–10 × (1, –7) = (–10 × 1, –10 × –7) = (–10, 70)$, where –10 is a scalar. Under these definitions for the operations, it can be rigorously proven that R2 is a …