dot and cross product

[nickdesaulniers]

Matrix A dot Matrix B

where the dot is usually a small circle (not sure if there's a unicode character for it)

cross product is also a peculiar x, but is not the same as matrix multiplication or component wise multiplication

[mattdesl]

Thanks, going to add dot/cross and multiplication notes above sigma.

In a lot of literature I see cross × being used to denote matrix multiplication. I have not seen Matrix A · B - any chance you can provide some examples? It seems a bit ambiguous - is it a dot product or just regular multiplication?

EDIT: Actually, I really only see matrix multiplication without any symbols, like: AB

[nickdesaulniers]

A · B is dot product, hence the 'dot operator'
The name "dot product" is derived from the centered dot " · " that is often used to designate this operation

A × B is cross product, see also its wiki

You're right about matrix multiplication being AB vs BA.

I cant remember if component wise multiplication has a symbol, but I also couldn't tell you when it's useful.

[allo-]

Componentwise is not used very much in math, because usually you choose the matrix because of the structure (i.e. having matvec and matmat products), not the representation. componentwise would be more like "let c be (a_1 b_1, ..., a_n b_n)" (or maybe c_ij = a_ij b=ij if you have 2D data for a reason), which does not per se have operations defined on it.

[mattdesl]

Yeah, I'm considering moving the element-wise vector multiplication out of that section since Hadamard is very specific and often uses different symbols.

Otherwise @nickdesaulniers do you think this issue is resolved with dot / cross? I think I will have to deal with matrices in their own section.

[nickdesaulniers]

Otherwise @nickdesaulniers do you think this issue is resolved with dot / cross?

LGTM