exterior product

Alex Berkovich — Wed, 21 Jan 2009 08:17:04 +0000

Greetings,

I wanted to ask -
Is there a built-in way of finding the exterior product (exterior power) of two vectors?

simple help doesn't find a thing. perhaps it is referred to in a different way?

Thanks a lot
Alex

Re: exterior product

Roger Stafford — Thu, 22 Jan 2009 18:13:01 +0000

"Alex Berkovich" <alexber@tx.technion> wrote in message <gl6lm0$lr7$1@fred.mathworks.com>...
> Greetings,
>
> I wanted to ask -
> Is there a built-in way of finding the exterior product (exterior power) of two vectors?
>
> simple help doesn't find a thing. perhaps it is referred to in a different way?
>
> Thanks a lot
> Alex

  I don't know of any built-in functions that cover all exterior products of vectors. In two dimensions there is 'det' which gives the scalar exterior product of two vectors as a 2 x 2 determinant. In three dimensional space there is 'cross' which gives the three-dimensional exterior product of two vectors. The exterior product (triple product) of three vectors is again given by 'det'. Each of these is extensively used in various matlab applications. I myself use them quite often.

  For higher dimensions the exterior products are defined over even higher dimensional spaces. The kth exterior product of k vectors in n dimensions is C(n,k)-dimensional. For example, the exterior product space of two vectors in four-dimensional space would be six-dimensional. I know of nothing in matlab which covers these. They must be created by the user in terms of other functions.

  (See http://en.wikipedia.org/wiki/Exterior_algebra)

Roger Stafford

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Re: exterior product