# Thread: What is a Rotated Transpose called?

1. ## What is a Rotated Transpose called?

Given a MATRIX

$\begin{pmatrix}
{a}&{b}&{c}&{d}\\
{e}&{f}&{g}&{h}\\
{i}&{j}&{k}&{l}\\
{m}&{n}&{o}&{p}
\end{pmatrix}$

The Transpose of a matrix rotates
the matrix about the DESCENDING diagonal.
The Transpose:

$\begin{pmatrix}
{a}&{e}&{i}&{m}\\
{b}&{f}&{j}&{n}\\
{c}&{g}&{k}&{o}\\
{d}&{h}&{l}&{p}
\end{pmatrix}$

Is there a name for the operation when
the matrix is rotated about the ascending diagonal?
The elements of the matrix are rotated clockwise 180 degrees,
then the reordered matrix is transposed.

$\begin{pmatrix}
{p}&{l}&{h}&{d}\\
{o}&{k}&{g}&{c}\\
{n}&{j}&{f}&{b}\\
{m}&{i}&{e}&{a}
\end{pmatrix}$

Is there a name for this operation?

Is there a site that explains (with graphics or images)
the different operations on matrices?

2. Originally Posted by aidan
Given a MATRIX

$\begin{pmatrix}
{a}&{b}&{c}&{d}\\
{e}&{f}&{g}&{h}\\
{i}&{j}&{k}&{l}\\
{m}&{n}&{o}&{p}
\end{pmatrix}$

The Transpose of a matrix rotates
the matrix about the DESCENDING diagonal.
The Transpose:

$\begin{pmatrix}
{a}&{e}&{i}&{m}\\
{b}&{f}&{j}&{n}\\
{c}&{g}&{k}&{o}\\
{d}&{h}&{l}&{p}
\end{pmatrix}$

Is there a name for the operation when
the matrix is rotated about the ascending diagonal?
The elements of the matrix are rotated clockwise 180 degrees,
then the reordered matrix is transposed.

$\begin{pmatrix}
{p}&{l}&{h}&{d}\\
{o}&{k}&{g}&{c}\\
{n}&{j}&{f}&{b}\\
{m}&{i}&{e}&{a}
\end{pmatrix}$

Is there a name for this operation?

Is there a site that explains (with graphics or images)
the different operations on matrices?
I have learnt the 1st transpose, but not the 2nd.
What is the uses of the 2nd transpose?

3. I'm not sure that it has a use.
I am trying to understand combinations/permutations, reflections, rotations, etc. of matrices, and was just wondering if the different
transformations have commonly accepted names.

My search has not been successful.