Exercise 2.2.9

Answers

It would be linear since for $c \in ℝ$ we have

T ((x_{1} + i y_{1}) + c (x_{2} + i y_{2})) = (x_{1} + c x_{2}) + i (x_{2} + c y_{2}) = T (x_{1} + i y_{1}) + cT (x_{2} + i y_{2}) .

And the matrix would be

(\begin{matrix} 1 & 0 \\ 0 & - 1 \end{matrix}) .

jephianlin

2011-06-27 00:00