Re: Re: RE: Re: Re: Non-comm

• To: mathgroup at smc.vnet.net
• Subject: [mg13488] Re: [mg13446] Re: [mg13414] RE: [mg13344] Re: [mg13280] Re: Non-comm
• From: Carl Woll <carlw at fermi.phys.washington.edu>
• Date: Sun, 26 Jul 1998 02:33:46 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I'm confused by the following:

> Regarding NonCommutativeMultiply:
>
> This feature doesn't solve any of the problems I mentioned.  As a
> trivial example, write 'NonCommutativeMultiply[I,A]' where 'I' is meant
> to represent the identity matrix.  You can't tell Mathematica that I
> and A are matrices, much less that I is the identity matrix, without
> defining the full-blown forms.  Mathematica assumes that I and A
> represent complex numbers.  So the matrix expression 'I A' will not
> simplify under NonCommutativeMultiply.

Mathematica has reserved the expression 'I' to represent the square root
of -1, so you don't want to use 'I' to represent the identity matrix.
On the other hand, 'A' is not reserved for anything, so in general it
does NOT represent a complex number.

As an alternative, you can use one of the other letter forms to
represent the identity matrix, for example, esc I esc, esc d s I esc,
or esc s c I esc would be fine, since Mathematica has not reserved
these expressions, and they look like the letter I. Or, you can just
use a name like Id.

At any rate, what is it that you want Mathematica to do with matrices.
Is it just as simple as having

I ** A

reduce to A? That is simple enough to program, and there are many ways
to do it. What else do you want Mathematica to do automatically with
matrices? Why don't you give some sample problems that you would like
to see solved, and somebody in the newsgroup may be able to provide a
solution or point out a package which can do what you want.

Carl Woll
Dept of Physics
U of Washington

On Fri, 24 Jul 1998, MJE wrote:

> Hi Ted -
>
> Regarding NonCommutativeMultiply:
>
> This feature doesn't solve any of the problems I mentioned.  As a
> trivial example, write 'NonCommutativeMultiply[I,A]' where 'I' is meant
> to represent the identity matrix.  You can't tell Mathematica that I
> and A are matrices, much less that I is the identity matrix, without
> defining the full-blown forms.  Mathematica assumes that I and A
> represent complex numbers.  So the matrix expression 'I A' will not
> simplify under NonCommutativeMultiply.
>
> Your comment about the Notation package is true in general terms, but
> for common things like symbolic matrix math, WRI should write the rule
> base, not every user on his own.
>
> Mark
>
>
> >
> > Isn't this built-in as a different type of multiplication?
> >
> > In[5]:=
> > ?NonCommutativeMultiply
> >
> > "a ** b ** c is a general associative, but non-commutative, form of \
> > multiplication."
> >
> > If you like you can use the Notation package to define a convention for
> > Input and/or Output that is more readable.
> >
> > Ted Ersek
> >
>
>

```

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