[R] Is there an easy way to generate linearly independent ve
(Ted Harding)
Ted.Harding at nessie.mcc.ac.uk
Fri Jun 18 10:15:38 CEST 2004
On 18-Jun-04 Fred wrote:
> I want to get linearly independent vectors, not orthogonal ones.
> The functions eigen, svd, I think it may provide orthogonal
> vectors which are not what I expect.
It depends what sort of characteristics you want your non-orthogonal
linearly independent vectors to have.
It's very easy to produce examples of such vectors: simple and
easy examples are like (e.g. for n=4)
1 0 0 0
1 1 0 0
1 1 1 0
1 1 1 1
or
1 0 0 0
1 1 0 0
0 1 1 0
0 0 1 1
and similar (all of which can be extended downwards arbitrarily
if you want n linearly independent vectors in k > n dimensions).
If these are too simplistic for you, please indicate how "interesting"
you want them to be.
The suggestions about using random numbers should work: it's not
likely that an NxN matrix of random numbers will be near singular,
so a test of the matrix to reject any which are too close is going
to be fairly efiicient.
E.g. you might consider a simple test like accepting the matrix M
if
max(abs(eigen(M)$values)))/min(abs(eigen(M)$values))) < 10
(the "10" is arbitrary, for illustration).
Hope this helps,
Ted.
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Date: 18-Jun-04 Time: 09:15:38
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