Eigensystem calculated for Integer versus Real numbers.
- To: mathgroup at smc.vnet.net
- Subject: [mg5383] Eigensystem calculated for Integer versus Real numbers.
- From: Wouter Meeussen <w.meeussen.vdmcc at vandemoortele.be>
- Date: Thu, 5 Dec 1996 14:50:22 -0500
- Sender: owner-wri-mathgroup at wolfram.com
hi all,
who can help me understand the difference between the Eigensystem as
calculated for Integer versus Real numbers :
define any integer symmetric matrix :
in m=(m=Table[Random[Integer,{0,1}],{3},{3}])+Transpose[m]
out {{2, 2, 0}, {2, 0, 2}, {0, 2, 2}}
be shure to pick one with non-zero determinant:
in Det[m]
out -16
in {val,vec}=Eigensystem[m]
out {{-2, 2, 4}, {{1, -2, 1}, {-1, 0, 1}, {1, 1, 1}}}
now, feed Eigensystem with reals:
in {nval,nvec}=Eigensystem[m//N]//Chop
out {{4., -2., 2.},
the ordering can be set 'right' by:
(left as an exercise to ...)
in {nval,nvec}=Transpose at Sort@Transpose at {nval,nvec}//Chop
out {{-2., 2., 4.},
at this point,both sets of eigenvectors are different by the factors :
(* cleanup . nvec == vec *)
in cleanup=vec.Inverse[nvec]//Chop
out {{2.44949, 0, 0},
{0, 1.41421, 0},
{0, 0, 1.73205}}
I could understand this in case of degeneracy (not all eigenvalues different),
but here ? Have I overlooked something ?
Check it out with this program, if you want :
program:=Module[{},m=(k=Table[Random[Integer,{0,4}],{3},{3}])+Transpose[k];
Wouter.
( baffled, as usual )
( and this is not a signature! )
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