From: MonkeeSage <MonkeeSage@...>
Date: 2006-09-12T10:35:37+09:00
Subject: Re: Matrix

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...