eigen 常用矩阵的操作

// 一些矩阵运算
    // 四则运算就不演示了，直接用+-*/即可。
    matrix_33 = Matrix3d::Random();      // 随机数矩阵
    cout << "random matrix: \n" << matrix_33 << endl;
    cout << "transpose: \n" << matrix_33.transpose() << endl;      // 转置
    cout << "sum: " << matrix_33.sum() << endl;            // 各元素和
    cout << "trace: " << matrix_33.trace() << endl;          // 迹
    cout << "times 10: \n" << 10 * matrix_33 << endl;               // 数乘
    cout << "inverse: \n" << matrix_33.inverse() << endl;        // 逆
    cout << "det: " << matrix_33.determinant() << endl;    // 行列式

    // 特征值
    // 实对称矩阵可以保证对角化成功
    SelfAdjointEigenSolver<Matrix3d> eigen_solver(matrix_33.transpose() * matrix_33);
    cout << "Eigen values = \n" << eigen_solver.eigenvalues() << endl;
    cout << "Eigen vectors = \n" << eigen_solver.eigenvectors() << endl;