16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.2.8

Linear Transformations

Mathematics — Linear Algebra · nilpotent-operator-range-null-space

Problem

Let

V

be a vector space over the field

F

and

T

a linear operator on

V

. If

T^2 = 0

, what can you say about the relation of the range of

T

to the null space of

T

? Give an example of a linear operator

T

R^2

such that

T^2 = 0

but

T \neq 0