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

**leesperare** · April 10th 2011, 07:40 PM

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 $A = \left| \begin{matrix} i & 1 & i \\<br /> 1 & i & i \end{matrix} \right|$ , compute $A^HA$ and $AA^H$ .

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

Please include all steps. Thank you!

**FernandoRevilla** · April 10th 2011, 10:07 PM

$A^H=(\bar{A})^t=\begin{bmatrix}{-i}&{\;\;1}&{-i}\\{\;\;1}&{-i}&{-i}\end{bmatrix}^t=\begin{bmatrix}{-i}&{\;\;1}&\\{\;\;1}&{-i}\\{-i}&{-i}\end{bmatrix}$

**leesperare** · April 11th 2011, 05:40 AM

Thank you! That really helped.

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

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

would $A^H =\begin{bmatrix}{1}&{1}&\\{-2i}&{-i}\\{-i}&{1-i}\end{bmatrix}$ ?

**FernandoRevilla** · April 11th 2011, 06:05 AM

Right.

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