Coordinate Vector - The Standard Representation

The Standard Representation

We can mechanize the above transformation by defining a function, called the standard representation of V with respect to B, that takes every vector to its coordinate representation: . Then is a linear transformation from V to Fn. In fact, it is an isomorphism, and its inverse is simply

Alternatively, we could have defined to be the above function from the beginning, realized that is an isomorphism, and defined to be its inverse.