Re: Question about matrix operations
- To: mathgroup at smc.vnet.net
- Subject: [mg42377] Re: [mg42366] Question about matrix operations
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Thu, 3 Jul 2003 06:10:32 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Wednesday, July 2, 2003, at 06:36 AM, Jeff Borski wrote: > Do you know of any way to find the basis and span of a group of vectors > using Mathematica? > > Thanks:) > > Jeff Borski I am not sure what you're after. There are an infinite number of bases for any vector space and I am not sure how you want the span represented since it is usually presented as a set of basis vectors. If you want an orthonormal basis for your space you can arrange your vectors as the columns of a matrix and use QRDecomposition. The rows of Q where R does not have a value of 0 on the diagonal form an orthonormal basis for the space spanned by your vectors. You can use NullSpace to find the kernel of your space. Regards, Ssezi PS - There is also the package LinearAlgebra`Orthogonalization` but you need to check that your vectors are linearly independent before using Gram-Schmidt orthogonalization.