The GENEIG subroutine computes eigenvalues and eigenvectors of a generalized eigenproblem.

The input arguments to the GENEIG subroutine are as follows:

sym-matrix1

is a symmetric numeric matrix.

sym-matrix2

is a positive definite symmetric matrix.

The subroutine returns the following output arguments:

evals

names a vector in which the eigenvalues are returned.

evecs

names a matrix in which the corresponding eigenvectors are returned.

The GENEIG subroutine computes eigenvalues and eigenvectors of the generalized eigenproblem. If and are symmetric and is positive definite, then the vector and the matrix solve the generalized eigenproblem provided that

The vector contains the eigenvalues arranged in descending order, and the matrix contains the corresponding eigenvectors in the columns.

The following example is from Wilkinson and Reinsch (1971):

A = {10   2   3   1   1,
      2  12   1   2   1,
      3   1  11   1  -1,
      1   2   1   9   1,
      1   1  -1   1  15};

B = {12   1  -1   2    1,
      1  14   1  -1    1,
     -1   1  16  -1    1,
      2  -1  -1  12   -1,
      1   1   1  -1   11};

call geneig(M, E, A, B);
print M, E;