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"
λ is an eigenvalue (a scalar) of the Matrix [A] if there is a non-zero vector (v) such that the following relationship is satisfied:
[A](v) = λ (v)Every vector (v) satisfying this equation is called an eigenvector of [A] belonging to the eigenvalue λ.
As an example, in the case of a 3 X 3 Matrix and a 3-entry column vector,
and each eigenvector v takes the form
To use this utility, you should have the a values ready to enter. If you have all the data ready, simply enter it, click the Solve button, and it will calculate the eigenvalues of [A]. Because the matrix is symmetric, the eigenvalues are real (assuming they can be computed).
HOW TO USE THIS UTILITY
Enter the appropriate data values for the A matrix.
(Taking advantage of the fact that A is symmetric, the user only has to input A values for entries along the diagonal and below the diagonal.)
Click the Solve button.
This utility will then calculate the eigenvalues of [A].
IMPORTANT: Note the Error Code. If it does not equal 0, some eigenvalues may not have been computed.
Enter the [A] values:
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.
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