Strange answer from Eigensystem[]!
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg839] Strange answer from Eigensystem[]!
- From: glandry at aol.com (GLandry)
- Date: Tue, 25 Apr 1995 02:20:25 -0400
- Organization: America Online, Inc. (1-800-827-6364)
I have a problem w/ the eigenvectors not being correct for
the simple nonsingular matrix A (shown below). All
eigenvalues seem correct. Two eigenvectors check, 2 don't..
WHY!!??
Also, using Mathcad, I get the same eigenvalues, but two
repeated eigenvectors (rounding off 10^-4 parts):
{.463I,0.117-0.773I,0.354+0.54I,0.212}
{-.463I,0.117+0.773I,0.354-0.54I,0.212}
The bizarre thing to me is these eigenvectors seem to check
too!?
Help! I must be missing some basic degeneracy. Unfortunately,
so in Mma.
****************************************
Gary Landry
glandry at aol.com
eelandry at utacnvx.uta.edu
________________
The University of Texas at Arlington
Department of Electrical Engineering
Box 19016
Arlington, TX 76019
****************************************
A={{0,0,0,1},{0,0,-1,0},{0,0.21,0,0},{-.21,0,0,0}};
MatrixForm[A]
0 0 0 1
0 0 -1 0
0 0.21 0 0
-0.21 0 0 0
{val,vec}=Eigensystem[A];
(Table[{A.vec[[i]],val[[i]] vec[[i]],
A.vec[[i]]==val[[i]] vec[[i]]},{i,4}])
-17
{{{4.17175 10 + 0. I, 0. + 0.416598 I, 0.190909 + 0. I,
0. + 0. I}, {0. + 0. I, 0. + 0.416598 I, 0.190909 + 0. I,
-17
0. + 1.91173 10 I}, False},
-17
{{4.17175 10 + 0. I, 0. - 0.416598 I, 0.190909 + 0. I,
0. + 0. I}, {0. + 0. I, 0. - 0.416598 I, 0.190909 + 0. I,
-17
0. - 1.91173 10 I}, False},
-312
{{0. + 1.95628 10 I, -1. + 0. I, 0. + 0. I, 0. + 0. I},
{0. + 0. I, 0. + 0. I, 0. - 0.458258 I, 0. + 0. I}, False},
-312
{{0. - 1.95628 10 I, -1. + 0. I, 0. + 0. I, 0. + 0. I},
{0. + 0. I, 0. + 0. I, 0. + 0.458258 I, 0. + 0. I}, False}}
Chop off "little" values, then the FIRST two work as solutions....
Cvec=Chop[vec];
(Table[{A.Cvec[[i]],val[[i]] Cvec[[i]],
A.Cvec[[i]]==val[[i]] Cvec[[i]]},{i,4}])
{{{0. + 0. I, 0. + 0.416598 I, 0.190909 + 0. I, 0. + 0. I},
{0, 0. + 0.416598 I, 0.190909 + 0. I, 0}, True},
{{0. + 0. I, 0. - 0.416598 I, 0.190909 + 0. I, 0. + 0. I},
{0, 0. - 0.416598 I, 0.190909 + 0. I, 0}, True},
{{0., -1., 0., 0.}, {0, 0, 0. - 0.458258 I, 0}, False},
{{0., -1., 0., 0.}, {0, 0, 0. + 0.458258 I, 0}, False}}