Subj : Re: Idea - Tensor could be modelled by 2 arrays and a function To : alt.math,alt.sci.physics,comp.programming From : Mr Pixie Date : Tue Aug 23 2005 06:56 pm "tadchem" wrote in message news:NtmdnZ2dnZ1qA6rdnZ2dnbCnl96dnZ2dRVn-zZ2dnZ0@comcast.com... > > "Mr Pixie" wrote in message > news:XxicnQxrrNewiJfeSa8jmA@karoo.co.uk... > > > > I used to program extensively in APL. > > In APL all variables are treated as arrays. Sounds like maybe a good language to do this in, although I don't have a copy of APL - don't know anything about it really - is it a free download? Since we're talking about a specific choice of language, my usual languages are VB.net or C#.net - I'd be interested to know how to do the Lorentz transform in either of those languages. I give the Lorenz tranform matrix here for reference: (gamma , -v * gamma , 0 , 0) ( -v * gamma , gamma, 0 , 0) La^b = ( 0 , 0 , 1 , 0) ( 0 , 0 , 0 , 1) where gamma = 1/((1-v^2)^0.5) so, if for the top row (the x0 dimension), the input is L^0 = (5,0,0,2), then we want to work out the sum: like so: L^0' = gamma*5 + (-0 * gamma)*0 + 0*0 + 0*2 = gamma*5 > Matrix inversion and transposition are monadic operators. I presume that means that the matrix operation in APL takes one argument and returns one result - is that going to be a problem if I want to model multi-linear forms (they would need many arguments)?? > I wrote a multivariate linear regression in one line. > > What could be simpler? > > Go read up on linear algebra. I was hoping I already know enough linear algebra to do this - I've been reading it for about 2 years! I would like to think I have a good enough knowledge of matrices, multi-linear forms & tensors already, but if you think I need to study some areas more, I'm willing to listen and will do it ;) > Tom Davidson > Richmond, VA > > .