Re:from Malta
- To: mathgroup at smc.vnet.net
- Subject: [mg27558] Re:from Malta
- From: bghiggins at ucdavis.edu (Brian Higgins)
- Date: Wed, 7 Mar 2001 04:07:55 -0500 (EST)
- Organization: The Math Forum
- References: <97l2tb$jf0@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
If you have a m by n matrix(A), then the fundamental theorem of linear
algebra relates the four subspaces associated with A:
Column space of A, nullspace of A, the column space of transpose(A)
and nullspace of transpose(A):
Thus
dim{column space of transpose(A) }+dim{nullspace of A}=n
dim{column space of A}+dim{nullspace of transpose(A)}=m
In mathematica the dimensions of the various subpaces can be found
using NullSpace, RowReduce
Thus dimension of nullspace is
Length[NullSpace[A]]
Dimension of the column space of A is
Length[DeleteCases[RowReduce[A], {0, 0, 0, 0}]]
or
Last[Dimensions[A]] - Length[NullSpace[A]]
Hope this helps,
Brian