MatrixXd X = MatrixXd::Random(4,4);
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MatrixXd A = X * X.transpose();
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cout << "Here is a random positive-definite matrix, A:" << endl << A << endl << endl;
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SelfAdjointEigenSolver<MatrixXd> es(A);
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MatrixXd sqrtA = es.operatorSqrt();
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cout << "The square root of A is: " << endl << sqrtA << endl;
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cout << "If we square this, we get: " << endl << sqrtA*sqrtA << endl;
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