Eigenvalues and Eigenvectors of a Symmetric Matrix

JACOBI_EIGENVALUE is a Python library which computes the eigenvalues and eigenvectors of a real symmetric matrix.

Given a real symmetric NxN matrix A, JACOBI_EIGENVALUE 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:

TEST_MAT, a Python 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:

Examples and Tests:

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Last revised on 25 September 2015.