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matrix
science forum beginner

Joined: 29 Dec 2005
Posts: 3

Posted: Thu May 25, 2006 2:24 pm    Post subject: Create subspace from Basis : Maple

Hi,
I have the Basis vectors of a subspace. How can I form the whole
subspace (all possible linear combinations) from these basis vectors in
Maple ?

I use symbolic computations mod 2.

Regards,
Narayanan Iyer
Julian V. Noble
science forum Guru Wannabe

Joined: 03 May 2005
Posts: 148

Posted: Thu May 25, 2006 6:12 pm    Post subject: Re: Create subspace from Basis : Maple

matrix wrote:
 Quote: Hi, I have the Basis vectors of a subspace. How can I form the whole subspace (all possible linear combinations) from these basis vectors in Maple ? I use symbolic computations mod 2. Regards, Narayanan Iyer

How can you possibly find all linear combinations in ANY program?
There is an uncountable infinity of them! Having the basis is the
same as having the subspace. The most you might do is orthogonalize
them, to be sure they are all linearly independent.

--
Julian V. Noble
Professor Emeritus of Physics
University of Virginia
Robert B. Israel
science forum Guru

Joined: 24 Mar 2005
Posts: 2151

Posted: Thu May 25, 2006 10:17 pm    Post subject: Re: Create subspace from Basis : Maple

matrix <iyerns@gmail.com> wrote:
 Quote: Hi, I have the Basis vectors of a subspace. How can I form the whole subspace (all possible linear combinations) from these basis vectors in Maple ? I use symbolic computations mod 2.

If your field is Z_2 (i.e. the integers mod 2), and the "vectors" are
implemented as lists or Vectors, then the span of a set of vectors V
can be obtained as follows:

 Quote: T:= combinat[cartprod]([seq]([0,1],i=V); n:= nops(V);

makevec:= proc(L) add(L[i]*V[i],i=1..n); % mod 2 end;
{seq}(makevec(T[nextvalue]()), i=1..2^n);

Note: if the set is not necessarily linearly independent, it's
better using lists here rather than Maple's Vectors,
because duplicate lists are automatically removed from a set, while
duplicate Vectors are not. Of course you can easily convert from
lists to Vectors or vice versa.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Stein Arild Str ømme
science forum beginner

Joined: 16 Aug 2005
Posts: 2

 Posted: Fri May 26, 2006 1:16 pm    Post subject: Re: Create subspace from Basis : Maple [Julian V. Noble] | matrix wrote: | > Hi, | > I have the Basis vectors of a subspace. How can I form the whole | > subspace (all possible linear combinations) from these basis vectors in | > Maple ? I use symbolic computations mod 2. Regards, Narayanan Iyer | > | | How can you possibly find all linear combinations in ANY program? | There is an uncountable infinity of them! Having the basis is the | same as having the subspace. The most you might do is orthogonalize | them, to be sure they are all linearly independent. Perhaps the OP has a finite field in mind. SA -- Stein Arild Strømme +47 55584825, +47 95801887 Universitetet i Bergen Fax: +47 55589672 Matematisk institutt www.mi.uib.no/stromme/ Johs Brunsg 12, N-5008 BERGEN stromme@mi.uib.no

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