Thread: What is a Rotated Transpose called?

1. What is a Rotated Transpose called?

Given a MATRIX

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

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

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

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.

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

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

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

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

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

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.

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

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.