C Eigenvalues Eigenvectors Tutorial

Finding eigenvalues and eigenvectors typically requires the use of numerical computation methods, with the most commonly used methods involving matrix operation libraries such as Eigen and LAPACK.

Here is an example code using the Eigen library to compute eigenvalues and eigenvectors.

#include <iostream>
#include <Eigen/Dense>

int main()
{
    Eigen::Matrix2d A;
    A << 1, 2,
         2, 1;
    
    Eigen::SelfAdjointEigenSolver<Eigen::Matrix2d> eigensolver(A);
    if (eigensolver.info() != Eigen::Success) {
        std::cerr << "Failed to compute eigenvalues and eigenvectors!" << std::endl;
        return 1;
    }

    std::cout << "The eigenvalues of A are:\n" << eigensolver.eigenvalues() << std::endl;
    std::cout << "The eigenvectors of A are:\n" << eigensolver.eigenvectors() << std::endl;

    return 0;
}

In the example code above, we start by defining a 2×2 matrix A and then use the SelfAdjointEigenSolver class from the Eigen library to calculate the eigenvalues and eigenvectors of A. Finally, we output the eigenvalues and eigenvectors of A.

It should be noted that the above code demonstrates how to use the Eigen library to calculate eigenvalues and eigenvectors. In real-world scenarios, larger matrices may be involved, so the code may need to be adjusted accordingly.