$AA^#=A^#A$ , Complex Matrices

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If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
$$A B A^#=A^#BA$$
for any $ntimes n$ complex matrix of functions $B$?



If not, when this result could be true?
Thanks in advance.







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    up vote
    1
    down vote

    favorite












    If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
    $$A B A^#=A^#BA$$
    for any $ntimes n$ complex matrix of functions $B$?



    If not, when this result could be true?
    Thanks in advance.







    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
      $$A B A^#=A^#BA$$
      for any $ntimes n$ complex matrix of functions $B$?



      If not, when this result could be true?
      Thanks in advance.







      share|cite|improve this question












      If $A$ is an $ntimes n$ invertible matrix of complex functions entries, with the property $AA^#=A^#A$ where $A^#(z)=left(overlineA(barz) right)^T$. Is it true that
      $$A B A^#=A^#BA$$
      for any $ntimes n$ complex matrix of functions $B$?



      If not, when this result could be true?
      Thanks in advance.









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 16 at 4:37









      John

      192




      192




















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          E.g. try
          $$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$






          share|cite|improve this answer




















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            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote













            E.g. try
            $$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$






            share|cite|improve this answer
























              up vote
              1
              down vote













              E.g. try
              $$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$






              share|cite|improve this answer






















                up vote
                1
                down vote










                up vote
                1
                down vote









                E.g. try
                $$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$






                share|cite|improve this answer












                E.g. try
                $$ A = pmatrixz+i & zcr z & z+icr, A^# = pmatrixz-i & zcr z & z-icr, B = pmatrix1 & 0cr 0 & 0cr $$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Aug 16 at 6:20









                Robert Israel

                305k22201443




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