1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathMatrixXcf A = MatrixXcf::Random(4,4); 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "Here is a random 4x4 matrix, A:" << endl << A << endl << endl; 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathComplexEigenSolver<MatrixXcf> ces; 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathces.compute(A); 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "The eigenvalues of A are:" << endl << ces.eigenvalues() << endl; 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "The matrix of eigenvectors, V, is:" << endl << ces.eigenvectors() << endl << endl; 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcomplex<float> lambda = ces.eigenvalues()[0]; 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "Consider the first eigenvalue, lambda = " << lambda << endl; 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan KamathVectorXcf v = ces.eigenvectors().col(0); 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl; 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "... and A * v = " << endl << A * v << endl << endl; 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathcout << "Finally, V * D * V^(-1) = " << endl 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath << ces.eigenvectors() * ces.eigenvalues().asDiagonal() * ces.eigenvectors().inverse() << endl; 17