Eigenvalues Calculator for a Real Symmetric Matrix
This page contains a routine that numerically finds the eigenvalues ONLY of a Real, Symmetric, Matrix. The algorithm is from the EISPACK collection of subroutines.
Smith, B.T.; J.M. Boyle; J.J. Dongarra; B.S. Garbow; Y. Ikebe; V.C. Klema; and C.B. Moler.
"Matrix Eigensystem Routines--(EISPACK) Guide"
Garbow, B.S.; J.M. Boyle; J.J. Dongarra; and C.B. Moler.
"Matrix Eigensystem Routines--(EISPACK) Guide Extension"
HOW TO USE THIS UTILITY
(i) The first entry should be the dimension of the system, N.
(ii) The next N x N entries should be the coefficients of the A Matrix.
The coefficients should be entered in the following order:
a11 a12 a13 . . .
a21 a22 a23 . . .
Do not enter commas, periods, brackets, etc. Also note that numbers in scientific notation are NOT recognized.
For example, say we want to compute the eigenvalues of a 3 x 3 matrix. Data should be input to the box as follows:
Then click the Compute button.
Note the Error Code. If it does not equal 0, some eigenvalues may not have been computed.
If Error Code > 0:
If more than 30 iterations are required to determine an eigenvalue, the subroutine terminates. The Error Code gives the index of the eigenvalue for which the failure occurred. Eigenvalues λ 1, λ 2, . . . λ ErCode - 1 should be correct.
For more information about this program, see the associated blog post: Eigenvalues Calculator of a Real Symmetric Matrix