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Topic: Intersection over an index
Replies: 3   Last Post: Oct 18, 2012 2:44 AM

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Sseziwa Mukasa

Posts: 108
Registered: 8/26/07
Re: Intersection over an index
Posted: Oct 18, 2012 2:43 AM
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Do you want the common eigenvectors or common eigenvalues?

Intersection@@Eigenvalues/@Table[A[k],{k,1,2}]

will give you the common eigenvalues (there are none)

Intersection@@Eigenvectors/@Table[A[k],{k,1,2}]

will give common eigenvectors (there are two), but if you work with machine precision arrays this probably won't work and you'll need to approximate the distance between eigenvectors, perhaps using the dot product, to decide if they are equal.

Regards,
Sseziwa

On Oct 16, 2012, at 8:12 PM, Geoffrey Eisenbarth wrote:

> Given a set of n many matrices A[k], I'd like to find any common eigenvectors. Using
>
> Intersection[Table[Eigenvalues[A[k]],{k,1,n}] doesn't seem to work. For instance:
>
> A[1] = {{-1, -3, 1}, {0, -3, 0}, {-1, -1, -1}};
> A[2] = {{-2, -1, 1}, {0, -1, 0}, {-1, 1, -2}};
> Intersection[Table[A[p], {p, 1, 2}]]
>
> gives me
> {{{-2, -1, 1}, {0, -1, 0}, {-1, 1, -2}}, {{-1, -3, 1}, {0, -3,
> 0}, {-1, -1, -1}}}
>
>
> Any suggestions?
>






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