"MonkeeSage" <MonkeeSage / gmail.com> wrote in message 
news:1158024640.933843.82830 / i42g2000cwa.googlegroups.com...
> 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...

    As far as I can tell, matrices are no different.  Your example shows 
that 1 is immutable but references to it can be re-assigned, so you can do:

n = 3
n = n + 1


    Matrices are no different and, so, you can do:


n = Matrix.scalar(2, 3)
n = n + Matrix.I(2)


    In both cases, the "number" types are immutable but the references to 
them are not, as you say.  They both work exactly the same way.  What are 
you trying to say?