What is a difference between linear operator and linear functional? Do I understand it correctly that linear operator is any operator that when applied on a vector from a vector space, gives again a vector from this vector space. And also obeys linearity conditions. And linear functional is a vector, dot product of which with the vector from the vector space gives again a vector from this vector space. And also linearity conditions are met. So, linear functional is a vector and linear operator is not a vector?