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Thread: What is a Rotated Transpose called?

  1. #1
    Super Member
    Joined
    Jan 2009
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    591

    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?
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  2. #2
    Member SengNee's Avatar
    Joined
    Jan 2008
    From
    Pangkor Island, Perak, Malaysia.
    Posts
    155
    Quote Originally Posted by aidan View Post
    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?
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  3. #3
    Super Member
    Joined
    Jan 2009
    Posts
    591
    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.
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