The vectors and are orthogonal, if .

If the vectors  all have unit norms in an vector system, then it is an orthonormal system.

The function has a local minimum at if there exists such that for any .

In an orthogonal system the vectors are all unit vectors and orthogonal to each other.

The scalar function is called the potential of the vector field if .

If then has a local maximum or a local minimum at .

Let be a smooth surface in and its boundary is the positively oriented curve . If is a continuously differentiable vector field, then

If is a critical point of the function and the principal minors of the Hessian are and , then has a maximum at .

If the function has a local minimum at , then it has also a minimum at .

If the partial derivatives of a function are zero at the point , then has a local minimum or local maximum at .