Question

what is A^(*) and B^(*)

Answer 1

\[A=\left[\begin{matrix}1+i & 2 \\ i & 1-3i\end{matrix}\right], \]

Answer 2

\[B=\left[\begin{matrix}i & 0 \\ 0& 2i\end{matrix}\right]\]

Answer 3

@zepdrix

Answer 4

first of all whats does \[A^*, B^* \] mean

Answer 5

I think `star` means `conjugate transpose`

Answer 6

\[\Large A=\left[\begin{matrix}1+i & 2 \\ i & 1-3i\end{matrix}\right]\]A transpose,\[\Large A^T=\left[\begin{matrix}1+i & i \\ 2 & 1-3i\end{matrix}\right],\]Conjugate of A,\[\Large \overline A=\left[\begin{matrix}1-i & 2 \\ -i & 1+3i\end{matrix}\right]\]So what do we get when we put these together? :)

Answer 7

you mean add them?

Answer 8

No, like just.. apply both rules :3

Answer 9

Which one you apply first, shouldn't matter

Answer 10

\[A^*=\left[\begin{matrix}1-i & -i \\ 2 & 1+3i\end{matrix}\right]\]

Answer 11

Mmm yay good job \c:/

Answer 12

so \[B^*= \left[\begin{matrix}-i & 0\\ 0& -2i\end{matrix}\right]\]

Answer 13

looks good! :)