1.Previous
3.Next

This is useful because it allows concrete calculations. Matrices yield examples of linear maps: if is a real matrix, then describes a linear map (see Euclidean space).

Let be a basis for . Then every vector is uniquely determined by the coefficients in the field :

If is a linear map,

which implies that the function f is entirely determined by the vectors . Now let be a basis for . Then we can represent each vector as

Thus, the function is entirely determined

1.Previous
3.Next