Transpose notation












0












$begingroup$


After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?



Question: Is there a reason for this notation? It's bothered me from since I learned it.






notation transpose







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$endgroup$












  • $begingroup$
    Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
    $endgroup$
    – J.G.
    Jan 6 at 17:05










  • $begingroup$
    In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
    $endgroup$
    – amd
    Jan 6 at 21:08










  • $begingroup$
    @J.G. What about T$(A)$
    $endgroup$
    – Benjamin Thoburn
    Jan 6 at 21:37
















0












$begingroup$


After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?



Question: Is there a reason for this notation? It's bothered me from since I learned it.






notation transpose







share|cite|improve this question









$endgroup$












  • $begingroup$
    Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
    $endgroup$
    – J.G.
    Jan 6 at 17:05










  • $begingroup$
    In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
    $endgroup$
    – amd
    Jan 6 at 21:08










  • $begingroup$
    @J.G. What about T$(A)$
    $endgroup$
    – Benjamin Thoburn
    Jan 6 at 21:37














0












0








0





$begingroup$


After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?



Question: Is there a reason for this notation? It's bothered me from since I learned it.






notation transpose







share|cite|improve this question









$endgroup$




After using the transpose for a while, I wondered if there in any vague connection to other superscript stuff like exponents or something. I doubt it, but I couldn't find anything and it seems weird to have it as a superscript. Is there anything deeper going on here?



Question: Is there a reason for this notation? It's bothered me from since I learned it.






notation transpose




notation transpose






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 6 at 13:34









Benjamin ThoburnBenjamin Thoburn

317111




317111












  • $begingroup$
    Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
    $endgroup$
    – J.G.
    Jan 6 at 17:05










  • $begingroup$
    In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
    $endgroup$
    – amd
    Jan 6 at 21:08










  • $begingroup$
    @J.G. What about T$(A)$
    $endgroup$
    – Benjamin Thoburn
    Jan 6 at 21:37


















  • $begingroup$
    Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
    $endgroup$
    – J.G.
    Jan 6 at 17:05










  • $begingroup$
    In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
    $endgroup$
    – amd
    Jan 6 at 21:08










  • $begingroup$
    @J.G. What about T$(A)$
    $endgroup$
    – Benjamin Thoburn
    Jan 6 at 21:37
















$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05




$begingroup$
Where else could we put the $T$? $A_T$ looks in the context of matrices like the $T$th component of a vector. I suppose we could use ${}^TA$ or ${}_TA$, or dispense with $T$ altogether with notation such as $bar{A}$. Good luck keeping track of the difference between transposes and Hermitian adjoints of complex matrices then, though.
$endgroup$
– J.G.
Jan 6 at 17:05












$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08




$begingroup$
In fact some sources do use ${}^TA$. Other sources use a prime to indicate the transpose, with the obvious potential for confusion.
$endgroup$
– amd
Jan 6 at 21:08












$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37




$begingroup$
@J.G. What about T$(A)$
$endgroup$
– Benjamin Thoburn
Jan 6 at 21:37










2 Answers
2






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1












$begingroup$

It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.



As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:




To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.







share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    If $A$ is a real orthogonal matrix, then
    $$A^{-1} = A^T$$



    This is the only little thing I can think of.






    share|cite|improve this answer









    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.



      As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:




      To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.







      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.



        As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:




        To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.







        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.



          As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:




          To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.







          share|cite|improve this answer









          $endgroup$



          It's just the conventional notation and is used for the conjugate transpose too: $mathbf A^mathsf {H}$.



          As the Wikipedia entry on the transpose of a matrix points out, you can use ${mathbf {A}}^{top}$ (top) instead of $mathbf {A}^{T}$ to make it stand out a bit better if that helps:




          To avoid confusing the reader between the transpose operation and a matrix raised to the $mathbf A^{th}$ power, the $mathbf {A}^{top}$ symbol denotes the transpose operation.








          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 6 at 17:25









          EdOverflowEdOverflow

          2059




          2059























              0












              $begingroup$

              If $A$ is a real orthogonal matrix, then
              $$A^{-1} = A^T$$



              This is the only little thing I can think of.






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                If $A$ is a real orthogonal matrix, then
                $$A^{-1} = A^T$$



                This is the only little thing I can think of.






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  If $A$ is a real orthogonal matrix, then
                  $$A^{-1} = A^T$$



                  This is the only little thing I can think of.






                  share|cite|improve this answer









                  $endgroup$



                  If $A$ is a real orthogonal matrix, then
                  $$A^{-1} = A^T$$



                  This is the only little thing I can think of.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 6 at 16:58









                  DamienDamien

                  58214




                  58214






























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