Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bob Hanlon

Posts: 906
Registered: 10/29/11
Re: Intersection over an index
Posted: Oct 18, 2012 2:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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?
>





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.