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Re: Intersection over an index
Posted:
Oct 18, 2012 2:42 AM
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intersectM[m1_?MatrixQ, m2_?MatrixQ] :=
Select[m2, MemberQ[m1, #] &];
intersectEV[m : {__?MatrixQ}] := Module[
{ev = Eigenvectors /@ m},
Fold[intersectM[#1, #2] &, First[ev], Rest[ev]]]
A[1] = {{-1, -3, 1}, {0, -3, 0}, {-1, -1, -1}};
Eigenvectors[A[1]]
{{1, 1, 1}, {-I, 0, 1}, {I, 0, 1}}
A[2] = {{-2, -1, 1}, {0, -1, 0}, {-1, 1, -2}};
Eigenvectors[A[2]]
{{-I, 0, 1}, {I, 0, 1}, {0, 1, 1}}
A[3] = {{-2, -1, -1}, {0, -1, 0}, {1, -1, -2}};
Eigenvectors[A[3]]
{{I, 0, 1}, {-I, 0, 1}, {0, -1, 1}}
A[4] = {{-2, -1, 1}, {0, -1, 0}, {1, -1, -2}};
Eigenvectors[A[4]]
{{-1, 0, 1}, {1, 0, 1}, {0, 0, 0}}
The first three have common eigenvectors
intersectEV[Table[A[k], {k, 3}]]
{{I, 0, 1}, {-I, 0, 1}}
Adding the fourth does not
intersectEV[Table[A[k], {k, 4}]]
{}
Bob Hanlon
On Tue, Oct 16, 2012 at 8:12 PM, Geoffrey Eisenbarth
<geoffrey.eisenbarth@gmail.com> 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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