Thread: Bases and Linear Maps

Hi, Quick question:


If I know that T:V -> W is injective and B is a basis of V, how can i use that to show that T(B) is a basis of W?

Thanks

Originally Posted by dr4g0n9

Hi, Quick question:


If I know that T:V -> W is injective and B is a basis of V, how can i use that to show that T(B) is a basis of W?

Thanks

You can't because it isn't true: is injective but not onto and thus no basis of the definition set can be mapped to a basis of the image set.

What is true is that if T is injective then the image of a basis is a lin. indep. set.

Tonio

edited