Standard Basis
The coordinate space Fn comes with a standard basis:
where 1 denotes the multiplicative identity in F. To see that this is a basis, note that an arbitrary vector in Fn can be written uniquely in the form
Read more about this topic: Coordinate Space
Famous quotes containing the words standard and/or basis:
“Error is a supposition that pleasure and pain, that intelligence, substance, life, are existent in matter. Error is neither Mind nor one of Mind’s 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 absurdity—namely, erroneous truth. Thus we should continue to lose the standard of Truth.”
—Mary Baker Eddy (1821–1910)
“Buddhists and Christians contrive to agree about death
Making death their ideal basis for different ideals.
The Communists however disapprove of death
Except when practical.”
—William Empson (1906–1984)