1c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochMatrixXd X = MatrixXd::Random(5,5); 2c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochMatrixXd A = X + X.transpose(); 3c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "Here is a random symmetric matrix, A:" << endl << A << endl; 4c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochX = MatrixXd::Random(5,5); 5c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochMatrixXd B = X * X.transpose(); 6c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "and a random postive-definite matrix, B:" << endl << B << endl << endl; 7c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdoch 8c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochGeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B); 9c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; 10c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; 11c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdoch 12c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochdouble lambda = es.eigenvalues()[0]; 13c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "Consider the first eigenvalue, lambda = " << lambda << endl; 14c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen MurdochVectorXd v = es.eigenvectors().col(0); 15c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl; 16c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdochcout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl; 17c5cede9ae108bb15f6b7a8aea21c7e1fefa2834cBen Murdoch