lapgeigh#

Purpose#

Computes generalized eigenvalues for a pair of real symmetric or Hermitian matrices.

Format#

ve = lapgeigh(A, B)#

Parameters:

A (NxN matrix) – real or complex symmetric or Hermitian matrix.
B (NxN matrix) – real or complex positive definite symmetric or Hermitian matrix.

Returns:

ve (Nx1 vector) – eigenvalues.

Examples#

// Assign A
A = { 3 4 5,
      2 5 2,
      3 2 4 };

// Assign B
B = { 4 2 2,
      2 6 1,
      2 1 8 };

// Find eigenvalues of the solution of the generalized
// symmetric eigenproblem  Ax = gBx
ve = lapgeigh(A, B);

// Print eigenvalues
print ve;

The code above returns:

1219
6787
9494

This procedure calls the LAPACK routines DSYGV and ZHEGV.

Remarks#

ve is the vector of eigenvalues of the solution of the generalized symmetric eigenproblem of the form \(Ax = λBx\).