Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I just want to verify that I'm on the right track for this:

If $T$ is the linear transformation $T: \mathbb{C} \to \mathbb{C}$ (where $\mathbb{C}$ is a vector space over $\mathbb{R}$, and $T(x) = (a + bi) \cdot x$, find the matrix that represents $T$ for the basis $\{1, i\}$.

So $T(1) = (a + bi) \cdot 1 = a + bi$ and $T(i) = ai + bi^2 = ai - b$, and therefore the matrix that represents $T$ is $\left( \begin{array}{c} a + bi \\ ai - b \end{array} \right)$?

Or is it a linear matrix? Or is it totally wrong?

share|cite|improve this question
up vote 2 down vote accepted

You should express the result in the basis $\{1,i\}$ as well, that is your matrix should be $\begin{bmatrix} a & b \\ -b & a\end{bmatrix}$.

share|cite|improve this answer
Right, makes sense, thanks! – user52610 Dec 11 '12 at 18:43

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.