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 …

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,...

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 …

Apr 13, 2017 · In some mathematical topics (probability transition matrices for Markov chains) the convention is typically a row vector times a matrix. Both of these are just special cases of matrix …

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 …

Sep 3, 2015 · 3 There are two basic ways you can multiply a vector, the dot product, as demonstrated in the link Dot Product, which gives you a scalar, no matter if you are multiplying A.B or squaring it, A.A. …

Feb 4, 2011 · On the other hand the dot product of two vectors gives the outcome of an operation applied on the vectors involved by considering the physics of the problem . Hence dot product of two …

Jan 24, 2015 · If you are looking for a multiplicative inverse, you should start thinking about vector multiplication and what the multiplicative identity is (or would be).

Mar 5, 2020 · Please help me understand the distinction between the two modes of multiplication: scalar multiplication and vector multiplication. What language is used to make the distinction between the …