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:

0.1219
0.6787
0.9494

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 \(Ax = λBx\).

See also

Functions lapgeig(), lapgeighv()