In linear function approximation one starts with a mapping that assigns a finite dimensional vector to each state-action pair.

Making things more generic, we can suggest that the function takes input as a 2-dimensional vector and outputs a one dimensional vector (scalar).

This is an -dimensional vector space whose elements can be thought of as equivalence classes of curves passing through the point .

Let denote i.i.d. normally distributed -dimensional random vectors with mean and covariance matrix .

Surface normals are three dimensional vectors of unit length.

The radar stations send the centre a six dimensional vector consisting of co-ordinates and velocities taken from the smoothing of discrete measurements.

It is supposed that the total potential energy of this system is proportional to the length of some -dimensional vector with all network segments as its components.

Any mental state can be described as an (N)-dimensional vector of numeric activation values over neural units in a network.

Example 2: Consider the problem of estimating the mean of dimensional Gaussian random vector, .