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.
Read more about this topic: Coordinate Vector
Famous quotes containing the word standard:
“Error is a supposition that pleasure and pain, that intelligence, substance, life, are existent in matter. Error is neither Mind nor one of Minds faculties. Error is the contradiction of Truth. Error is a belief without understanding. Error is unreal because untrue. It is that which seemeth to be and is not. If error were true, its truth would be error, and we should have a self-evident absurditynamely, erroneous truth. Thus we should continue to lose the standard of Truth.”
—Mary Baker Eddy (18211910)