# Finding a Hermitian Matrix A^H for a 2 x 3 Matrix A

• Apr 10th 2011, 07:40 PM
leesperare
Finding a Hermitian Matrix A^H for a 2 x 3 Matrix A
Hello,

I'm having a really hard time with Hermitian matrices.

In preparation for my exam next week, I've been trying to figure out this problem:

Given a matrix $\displaystyle A = \left| \begin{matrix} i & 1 & i \\ 1 & i & i \end{matrix} \right|$, compute $\displaystyle A^HA$ and $\displaystyle AA^H$.

How do I find $\displaystyle A^H$ given the 2x3 matrix $\displaystyle A$?

Please include all steps. Thank you!
• Apr 10th 2011, 10:07 PM
FernandoRevilla
$\displaystyle A^H=(\bar{A})^t=\begin{bmatrix}{-i}&{\;\;1}&{-i}\\{\;\;1}&{-i}&{-i}\end{bmatrix}^t=\begin{bmatrix}{-i}&{\;\;1}&\\{\;\;1}&{-i}\\{-i}&{-i}\end{bmatrix}$
• Apr 11th 2011, 05:40 AM
leesperare
Thank you! That really helped.

I've moved on to another similar problem, and want to make sure I have the correct $\displaystyle A^H$.

If given matrix $\displaystyle A = \begin{bmatrix}{1}&{2i}&{i}\\{1}&{i}&{1+i}\end{bma trix}$ ,

would $\displaystyle A^H =\begin{bmatrix}{1}&{1}&\\{-2i}&{-i}\\{-i}&{1-i}\end{bmatrix}$ ?
• Apr 11th 2011, 06:05 AM
FernandoRevilla
Right.