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1 | MatrixXd X = MatrixXd::Random(5,5);
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2 | MatrixXd A = X + X.transpose();
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3 | cout << "Here is a random symmetric 5x5 matrix, A:" << endl << A << endl << endl;
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4 |
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5 | SelfAdjointEigenSolver<MatrixXd> es(A);
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6 | cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
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7 | cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
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8 |
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9 | double lambda = es.eigenvalues()[0];
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10 | cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
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11 | VectorXd v = es.eigenvectors().col(0);
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12 | cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
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13 | cout << "... and A * v = " << endl << A * v << endl << endl;
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14 |
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15 | MatrixXd D = es.eigenvalues().asDiagonal();
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16 | MatrixXd V = es.eigenvectors();
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17 | cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
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