16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 3.1.10

Linear Transformations

Mathematics — Linear Algebra · real-linear-not-complex-linear

Problem

Let

V

be the set of all complex numbers regarded as a vector space over the field of real numbers (usual operations). Find a function from

V

into

V

which is a linear transformation on the above vector space, but which is not a linear transformation on

C^1

, i.e., which is not complex linear.