- #1

- 532

- 5

## Main Question or Discussion Point

Hey I'd appreciate it if somebody could "yay or nay" my understanding of the following concepts, I think I'm mixing something up.

[tex] 1. Complex Matrix [/tex]

[tex] A =

\begin{bmatrix}

1 & 1 + i & 2 + i \\

2 + 3i & 4 - i & 3 + 2i

\end{bmatrix}

[/tex]

[tex] 2. Complex Conjugate Matrix [/tex]

[tex] \overline{A} =

\begin{bmatrix}

1 & 1 - i & 2 - i \\

2 - 3i & 4 + i & 3 - 2i \end{bmatrix} [/tex]

[tex] 3. Transpose Matrix [/tex]

[tex] A^T =

\begin{bmatrix}

1 & 2 - 3i \\

1 - i & 4 + i\\

2 - i & 3 - 2i

\end{bmatrix} [/tex]

[tex] 4. Conjugate Transpose Matrix [/tex]

[tex] \overline{A}^T =

\begin{bmatrix}

1 & 2 + 3i \\

1 + i & 4 - i\\

2 + i & 3 + 2i

\end{bmatrix} [/tex]

I think these last two may be confused or maybe even the 4th one is just my invention.

I'd appreciate a word of comment should any corrections be required.

[tex] 1. Complex Matrix [/tex]

[tex] A =

\begin{bmatrix}

1 & 1 + i & 2 + i \\

2 + 3i & 4 - i & 3 + 2i

\end{bmatrix}

[/tex]

[tex] 2. Complex Conjugate Matrix [/tex]

[tex] \overline{A} =

\begin{bmatrix}

1 & 1 - i & 2 - i \\

2 - 3i & 4 + i & 3 - 2i \end{bmatrix} [/tex]

[tex] 3. Transpose Matrix [/tex]

[tex] A^T =

\begin{bmatrix}

1 & 2 - 3i \\

1 - i & 4 + i\\

2 - i & 3 - 2i

\end{bmatrix} [/tex]

[tex] 4. Conjugate Transpose Matrix [/tex]

[tex] \overline{A}^T =

\begin{bmatrix}

1 & 2 + 3i \\

1 + i & 4 - i\\

2 + i & 3 + 2i

\end{bmatrix} [/tex]

I think these last two may be confused or maybe even the 4th one is just my invention.

I'd appreciate a word of comment should any corrections be required.

**5**: What does [tex] A^* [/tex] usually signify, is it the complex conjugate or the complex transpose (assuming it exists).