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! ) NV Vandemoortele Coordination Center Group R&D Center Prins Albertlaan 79 Postbus 40 B-8870 Izegem Tel: +/32/51/33 21 11 Fax:+32/51/33 21 75 vdmcc at vandemoortele.be