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:
“Any honest examination of the national life proves how far we are from the standard of human freedom with which we began. The recovery of this standard demands of everyone who loves this country a hard look at himself, for the greatest achievments must begin somewhere, and they always begin with the person. If we are not capable of this examination, we may yet become one of the most distinguished and monumental failures in the history of nations.”
—James Baldwin (1924–1987)