From: Rick DeNatale <rick.denatale@...>
Date: 2006-09-12T10:52:28+09:00
Subject: Re: Matrix

On 9/11/06, MonkeeSage <MonkeeSage@gmail.com> wrote:
> Dave Burt wrote:
> > If you want a matrix-like data structure (rather than a mathematical
> > matrix), why not use an array of arrays?
>
> A mathematical matrix is just a dimensional arrangement of data into
> "rows" and "columns", thus allowing for certain algorithmic
> relationships to be defined and applied (e.g., canonical
> decompositions). Every matrix (i.e., the actual matrix considered as a
> complex value) is immutable and has a unique identity, just like every
> number -- that's true -- but they can also be permuted or otherwise
> transformed into different matrices. Why should one have to do that
> constructively (i.e., construct a new matrix "from scratch"), rather
> than destructively (i.e., change the existing matrix "in place"). Think
> of it like this: n = 1; n = n + 1 -- even though the number 1 is
> immutable and has a unique identity, the reference to it is not, and
> can thus be destructively altered by assignment with the result that it
> refers to new identity. It would be a pain to have to do o = n + 1, p =
> n + 2 (i.e., creating new references every time the data changes), just
> because 1 is immutable. Why should a matrix be any different? Mabye I'm
> missing something...

Yes, you're missing the distinction between a variable which
references a sequence of objects over time, and the objects it
references.

a = 1
a = 2

Does NOT change 1 to 2.

Fortran II used to let you change 1 to 2:

subroutine a(arg)
   arg = 2
end subroutine a

call a(1)

But this was considered a bug and was changed in Fortran IV.


-- 
Rick DeNatale

My blog on Ruby
http://talklikeaduck.denhaven2.com/