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

The vector field is conservative if and only if its line integral is path independent, that is if and have common starting and ending points, then

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

If is an eigenvector of the linear transformation , then .

A vector field is conservative if and only if there exists a closed curves such that

The function has a minimum at , if for any .

One has the following relationship between the scalar product and the norm: .

The random variable is called continuous, if there exists a function such that the cumulative distribution function can be expressed as

The divergence of is

The line integral of the scalar field along the curve is