jacobi_eigenvalue, a FORTRAN77 code which uses the Jacobi iteration to compute the eigenvalues and eigenvectors of a real symmetric matrix.

Given a real symmetric NxN matrix A, the routine carries out an iterative procedure known as Jacobi's iteration, to determine a N-vector D of real, positive eigenvalues, and an NxN matrix V whose columns are the corresponding eigenvectors, so that, for each column J of the eigenmatrix:

        A * Vj = Dj * Vj


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


jacobi_eigenvalue is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

EISPACK, a FORTRAN77 library which carries out eigenvalue computations; superseded by LAPACK;


LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.

TEST_EIGEN, a FORTRAN77 library which implements test matrices for eigenvalue analysis.

TEST_MAT, a FORTRAN77 library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.


  1. Gene Golub, Charles VanLoan,
    Matrix Computations, Third Edition,
    Johns Hopkins, 1996,
    ISBN: 0-8018-4513-X,
    LC: QA188.G65.

Source Code:

Last revised on 26 February 2021.