Cross product can refer to the application of the multiplication operator to each element of the Cartesian cross product of two sets. When used this way, it is the same as what would normally be called outer product.
But I completely agree with Dmitriy that more people are going to understand the name "outer product" correctly than the name cross product. On Sun, Dec 25, 2011 at 4:07 PM, Dmitriy Lyubimov <[email protected]> wrote: > Wikipedia seems to disagree. I also knew it the same way as wikipedia > states, before. > > http://en.wikipedia.org/wiki/Cross_product > > > > On Sun, Dec 25, 2011 at 3:39 PM, Raphael Cendrillon > <[email protected]> wrote: > > I think the cross product is typically used to refer to the outer > product, while the dot product refers to the inner product. > > > > On Dec 25, 2011, at 2:51 PM, Ted Dunning <[email protected]> wrote: > > > >> This is misleading even if not strictly incorrect. In matrix > terminology, > >> outer product is definitely more commonly used. > >> > >> On Sun, Dec 25, 2011 at 1:37 PM, Dmitriy Lyubimov <[email protected]> > wrote: > >> > >>> Hello, > >>> > >>> just stumbled on this in vector while looking for outer product > operation > >>> -- > >>> > >>> @Override > >>> public Matrix cross(Vector other) { > >>> Matrix result = matrixLike(size, other.size()); > >>> for (int row = 0; row < size; row++) { > >>> result.assignRow(row, other.times(getQuick(row))); > >>> } > >>> return result; > >>> } > >>> > >>> > >>> It seems this guy computes an outer product, but not cross product ( > >>> crossprod for vectors =ab sin(theta)n). Seems like a misleading > >>> naming. > >>> > >>> It is probably motivated by R, where tcrossproduct (which is a product > >>> of matrices, not vectors) is defined as XY' and crossprod which is > >>> defined X'Y and so in case of cbind(vector) it would constitute either > >>> dot product or outer product respectively. But i am not sure where R > >>> is deriving this; and even then it is definitely misleading as R would > >>> apply this to the world of matrices, not vectors. In vectors cross > >>> product means something else and i think this may create a confusion > >>> (it certainly did in my case).. > >>> > >>> thanks. > >>> -Dmitriy > >>> >
