16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.1.13

Linear Transformations

Mathematics — Linear Algebra · equivalent-conditions-linear-operator

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