16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.1.12

Linear Transformations

Mathematics — Linear Algebra · range-null-space-identical-even-dimension

Problem

Let

V

be an

n

-dimensional vector space over the field

F

and let

T

be a linear transformation from

V

into

V

such that the range and null space of

T

are identical. Prove that

n

is even. (Can you give an example of such a linear transformation

T