Re: Intersection over an index

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• Subject: [mg128425] Re: Intersection over an index
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Thu, 18 Oct 2012 02:37:47 -0400 (EDT)
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```On 10/16/12 at 8:12 PM, geoffrey.eisenbarth at gmail.com (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?

The problem with your approach is Intersection wants two or more
lists and you are supplying only one list. I would do what you
want as follows:

In[1]:= a = {{-1, -3, 1}, {0, -3, 0}, {-1, -1, -1}};
b = {{-2, -1, 1}, {0, -1, 0}, {-1, 1, -2}};

In[3]:= Intersection @@ (Eigenvectors /@ {a, b})

Out[3]= {{-I, 0, 1}, {I, 0, 1}}

But if you favor defining a function as you did above to return
matrices and want to use Table, then the same result can be
obtained with:

In[4]:= x[1] = a; x[2] = b;
Intersection @@ Table[Eigenvectors[x@n], {n, 2}]

Out[5]= {{-I, 0, 1}, {I, 0, 1}}

```

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