Re: Intersection over an index

*To*: mathgroup at smc.vnet.net*Subject*: [mg128420] Re: Intersection over an index*From*: Sseziwa Mukasa <mukasa at gmail.com>*Date*: Thu, 18 Oct 2012 02:36:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20121017001211.0C48B685E@smc.vnet.net>

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? >

**References**:**Intersection over an index***From:*Geoffrey Eisenbarth <geoffrey.eisenbarth@gmail.com>