# [Maxima] vector times vector; vector^-1?

van Nek van.nek at arcor.de
Sat Nov 15 14:39:24 CST 2008

```Using a new definition v: vector(1,2) there is no builtin simplification which tells you what v.v
should be and you can define what seems to be the best. And in addition there would be no
need to change the existing dot product. The development of vectors can be done
separately.

Volker

Am 15 Nov 2008 um 14:59 hat Viktor T. Toth geschrieben:

> On the topic of multiplying vectors and matrices, I've been meaning to make
> a suggestion: I think it might be a good idea to modify the dot product
> (perhaps tied to a global variable <groan> that determines if this new
> behavior is to be used) to allow the ELEMENTS of the matrices or vectors
> involved to be noncommutative.
>
> At present, for instance, a lot of quantum physics problems cannot be
> tackled in the "natural way" in Maxima, because they involve matrices with
> nonscalar elements, yet Maxima insists on commutative multiplication.
>
> To be clear about it, what I am proposing is that (optionally, perhaps)
>
> [a,b].[c,d]
>
> should return
>
> a.c + b.d
>
>
> ac + bd
>
> which it does at present. Of course if, say, both a and b are declared
> scalars, returning ac + bd should be fine.
>
>
> Viktor
>
>
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
> On Behalf Of Robert Dodier
> Sent: Saturday, November 15, 2008 2:28 PM
> To: van Nek
> Cc: Maxima at math.utexas.edu
> Subject: Re: [Maxima] vector times vector; vector^-1?
>
> On 11/15/08, van Nek <van.nek at arcor.de> wrote:
>
> >  I am just coding a new definiton of a vector and some basic vector
> > simplifications and functions.
>
> Thanks for working on this topic. I think it is very important.
>
> >  At the moment I wonder what vector * vector and vector ^ -1should be.
>
> If I am not mistaken, these are typically not defined in vector algebra.
> Therefore they should not be defined in Maxima's vector operations either.
> But these should not cause an error; Maxima should  just let them be.
>
> There is a lot of temptation to add convenience functions,
> but at least for vectors, we should resist the temptation.
> In the long run it will be more difficult to use Maxima vectors,
> if they do not have the same algebraic properties as mathematical vectors.
>
> By the way, I think that creating a new vector object is the
> right way to proceed, instead of making them lists or matrices,
> which have different properties.
>
> Thanks for your help, & please keep up the good work.
>
> Robert Dodier
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```