Troubleshooting - A Guide to MATLAB for Beginners and Experienced Users - page 261

A1*U1 - U1*R1

ans =
1.0e-014 *
0.3109

0.2554 - 0.3553i 0.2554 + 0.3553i

-0.0333 -0.1776 - 0.3220i -0.1776 + 0.3220i

-0.0833 -0.1721 - 0.0444i -0.1721 + 0.0444i

This is essentially zero. Notice the " e-014 " .

[U2, R2] = eig(A2)

U2 =
0.9669

0.7405 0.7405

0.1240 0.4574 - 0.2848i 0.4574 + 0.2848i

-0.2231 0.2831 + 0.2848i 0.2831 - 0.2848i

R2 =
-0.0000 0 0

0 0.5000 + 6.5383i 0

0 0 0.5000 - 6.5383i

A2*U2 - U2*R2

ans =
1.0e-014 *
-0.3154

-0.3331 - 0.4441i -0.3331 + 0.4441i

-0.2423 0.0888 + 0.3109i 0.0888 - 0.3109i

-0.1140 -0.0222 + 0.2665i -0.0222 - 0.2665i

This is essentially zero as well.

[U3, R3] = eig(A3)

U3 =
-0.2446 - 0.4647i -0.2446 + 0.4647i 0.5621 - 0.1062i
0.5621 + 0.1062i
0.6254

0.6254 -0.1982 - 0.0654i -

0.1982 + 0.0654i
0.0025 + 0.3017i 0.0025 - 0.3017i 0.5833