Question:

If T is a linear operator on a vector space V(F) such that (zero map), then show that T is invertible.

i know that to show invertible i have to show 1-1 and onto, but i have no idea how to begin showing this ... any help?

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- Aug 14th 2011, 08:48 AMibnashraftransformation question
Question:

If T is a linear operator on a vector space V(F) such that (zero map), then show that T is invertible.

i know that to show invertible i have to show 1-1 and onto, but i have no idea how to begin showing this ... any help? - Aug 14th 2011, 10:34 AMModusPonensRe: transformation question
. Now see if the kernel has any vectors different from zero.

- Aug 14th 2011, 10:46 AMHallsofIvyRe: transformation question
Slight variation:

- Aug 14th 2011, 11:04 AMModusPonensRe: transformation question
Can you commute T and I-T?

- Aug 14th 2011, 01:40 PMHallsofIvyRe: transformation question
Yes, of course: . Any linear operator from a vector space to itself commutes with itself and the identity.

- Aug 14th 2011, 05:45 PMDrexel28Re: transformation question