16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.7.4

Linear Transformations

Mathematics — Linear Algebra · eigenvector-transpose-functional

Problem

Let

V

be a finite-dimensional vector space over the field

F

and let

T

be a linear operator on

V

. Let

c

be a scalar and suppose there is a non-zero vector

\alpha

V

such that

T\alpha = c\alpha

. Prove that there is a non-zero linear functional

f

V

such that

T^t f = cf