Re:Calculize: A Mathematical Scripting Language
by sesqu on Thursday August 11, 2011 @07:17PM
(#2875259)
Right. And how would you characterize the 4-dimensional extension, in terms of the first three?
Or do you simply draw the line at two dimensions, figuring that's as much as anyone will ever need?
Re:Calculize: A Mathematical Scripting Language
by JadeNB on Tuesday August 23, 2011 @04:29PM
(#2918244)
What are the two dimensions of which you speak here? The 'row' and 'column' dimensions of a matrix? If so, that's exactly what tensors do: A matrix is a 2-tensor (better, a (1, 1)-tensor, but let's not get into that). If you want an m-dimensional generalisation, just use an m-tensor.
Vectors are a special case of matrices, which are a special case of tensors (finally, scalars, which is just a fancy name for plain numbers, are a special case of vectors). Although there are many mathematical representation of all these objects (geometrical, functional, etc.), they can be written as multidimensional arrays (after selecting for a base).
Thus, scalars are 1x1 matrices, and a vector of size n is actually a nx1 matrix. Although a common high-school notation of a vector is x = (1, 2, 3), a vector is actually
Tensors are the extension of matrices to further dimensions.