norm() is the Frobenius norm, the square root of the sum of squares of the components..normalized() returns a copy to the original object divided by this norm (i.e. the original object is not changed)..normalize() divides an object in-place by this norm (i.e. the original object itself is modified).
Code Example §
Eigen::Vector3d vectorA(1.0, 2.0, 3.0);
auto vectorA_norm = vectorA.norm(); // = 3.74166
// equivalent to sqrt(1*1+2*2+3*3)
auto clone_vectorA = vectorA;
auto normalized_vectorA = vectorA.normalized();
// vectorA == clone_vectorA;
vectorA.normalize();
// vectorA != clone_vectorA;
https://stackoverflow.com/questions/48019329/difference-between-norm-normalize-and-normalized-in-eigen