## 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.

**References:**

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"

Springer-Verlag, Berlin.

1976

Garbow, B.S.; J.M. Boyle; J.J. Dongarra; and C.B. Moler.

"Matrix Eigensystem Routines--(EISPACK) Guide Extension"

Springer-Verlag, Berlin.

1977

The original sub-routines were written in FORTRAN and have been translated to Javascript here. Although all care has been taken to ensure that the sub-routines were translated accurately, some errors may have crept into the translation. These errors are mine; the original FORTRAN routines have been thoroughly tested and work properly. Please report any errors to the webmaster.

**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:

a_{11} a_{12} a_{13} . . .

a_{21} a_{22} a_{23} . . .

etc.

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:

3 | ||

25 | 15 | -5 |

15 | 18 | 0 |

-5 | 0 | 11 |

Then click the **Compute** button.

**IMPORTANT!**

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