Consider the problem of transferring a unit mass at rest sliding on a plane from a point to another at a unit distance. We can exert a constant force of magnitude on the mass at time intervals , .

Denoting by the position at the final instant , we can express via Newton’s law the relationship between the force vector and position/velocity vector as , where .

Now assume that we would like to find the smallest-norm (in the Euclidean sense) force that puts the mass at at the final time. This is the problem of finding the minimum-norm solution to the equation . The solution is .