Kunze Linear Algebra · Problem 3.1.13

Linear Transformations

Mathematics — Methods · range-null-space-intersection

Problem

Let

V

be a vector space and

T

a linear transformation from

V

into

V

. Prove that the following two statements about

T

are equivalent. (a) The intersection of the range of

T

and the null space of

T

is the zero subspace of

V

. (b) If

T(T\alpha) = 0

, then

T\alpha = 0