why are there only two methods of vector multiplication?
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 …
What is really meant by the product of two vectors?
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 …
Element-wise (or pointwise) operations notation?
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 …
matrix-vector multiplication - Mathematics Stack Exchange
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.
Vector Multiplication with Multiple Kronecker Products
Aug 3, 2016 · Shuffle algorithm (Plateau, 1985) is an efficient vector-Kronecker product algorithm that can be used to compute multiplication of a vector and Kronecker product of rectangular matrices. …
Dot product vs Matrix multiplication, is the later a special case of ...
Long story short, the question is simple. Is matrix multiplication just a special case of the dot product of two sets of vectors when the sets of vectors have the same cardinality and all vectors in both sets …
notation - Symbol for elementwise multiplication of vectors ...
I recommend writing componentwise multiplication of vectors using some symbol that does not have a standard meaning, perhaps ⋆ ⋆ (\star) or ⋄ ⋄ (\diamond), so that people reading won't have any …
Product between a column vector and a row vector
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 …
linear algebra - Notation for element-wise division of vectors ...
I am wondering if there is any standard notation for the element-wise division of vectors. I am going to use ⊘ ⊘ for this purpose, similar to ⊙ ⊙ that is used in some texts for element-wise multiplication. …
Why don't we define vector multiplication component-wise?
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,...