Hi,

Can a linear trans. T:V-->W be 1 to 1 if Ker(T) != {the zero vector on V}?

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- Apr 24th 2012, 02:27 AMjfkAbout 1-1 Linear Transformations
Hi,

Can a linear trans. T:V-->W be 1 to 1 if Ker(T) != {the zero vector on V}? - Apr 24th 2012, 03:06 AMemakarovRe: About 1-1 Linear Transformations
If v ∈ Ker(T) where v ≠ 0, then T(v) = T(0) = 0, so...

By the way, the question should probably say, "Ker(T) != {the zero vector on**V**}" because Ker(T) ⊆ V. - Apr 24th 2012, 05:53 AMHallsofIvyRe: About 1-1 Linear Transformations
In fact, if f(v)= 0 (for $\displaystyle v\ne 0$) if u- w= v then it is also true that f(u)= f(v).