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Re: Arbitrary vector

• To: mathgroup at smc.vnet.net
• Subject: [mg121644] Re: Arbitrary vector
• From: Jacopo Bertolotti <jacopo.bertolotti at gmail.com>
• Date: Sat, 24 Sep 2011 22:30:45 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201109230742.DAA07655@smc.vnet.net>

Hi,
I have the feeling that your question is ill posed. A vector is (by 
definition) an element of a vector space and a vector space is just a 
set where certain properties are defined/respected (e.g. a commutative 
addition between the elements is defined etc.). Some vectors can be 
represented as a list of numbers (e.g. velocity) and some can not (e.g. 
square integrable functions).
If all you are interested in are those vectors that can be represented 
as lists of numbers and you are happy with the canonical operations 
(scalar product, multiplication by a matrix, outer product etc.) then 
the problem is non-existent since Mathematica do it automatically.
To be more clear: a.b is interpreted as the scalar product between the 
two vectors/matrices/tensors a and b irrespectively from their number of 
elements. If the operation is impossible (say a has three components and 
b 4) you will get an error but nothing more.
Of course do not expect any smart simplification or algebraic trick from 
Mathematica unless you impose some assumptions.

Jacopo

p.s.
If I misunderstood your question could you just try to reformulate it?


On 09/23/2011 09:42 AM, James Womack wrote:
> Hello,
>
> Does anyone know if it is possible to define an arbitrary vector in
> Mathematica? What I mean by this, is can I tell Mathematica that a
> particular variable is a vector, without having to define the components
> of this vector?
>
> I'd like to be able to manipulate vectors with an arbitrary number of
> components, but am not sure if this is possible in Mathematica.
>
> Many thanks,
> James
>
>

• References:
  • Arbitrary vector
    • From: James Womack <james.c.womack@gmail.com>