Kunze Linear Algebra · Problem 6.7.3

Elementary Canonical Forms

Mathematics — Methods · range-null-space-independent-direct-sum

Problem

Let

T

be a linear operator on a finite-dimensional vector space

V

. Let

R

be the range of

T

and let

N

be the null space of

T

. Prove that

R

and

N

are independent if and only if

V = R \oplus N