Mar 26, 2015 · If you add additional structure to the vector space by giving meaning to products of the form $\vec {v}a$, that's fine, but it's not part of the underlying vector space structure. It's a …

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 …

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 …

Dec 15, 2017 · I know that matrices product is correct when the number of the columns of the first matrix is equal to the number of rows of the second matrix. Why I can't do the product …

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), …

Note, though, that $a$ is a column vector, but $a^T$ is a row vector. The dot product is only defined for two vectors of the same type, so your expressions $a^T\cdot a$ and $a\cdot a^T$ …

I cannot find a way to prove it You have an explicit formula (I'm assuming, of course, the naive matrix multiplication algorithm) with additions and multiplications in it, and you have a …

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 …

Mar 12, 2014 · And each of these vectors has length one. So you're looking for something that can multiply 1 to get 0 in one case, and can multiply 1 to get 1 in the other. There ain't no such …

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 …