Canonical form of pairs of matrices over arbitrary field

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I'm looking for a canonical form of pairs of matrices over arbitrary field up to equivalence (Calling pairs ($A, B$) and ($A_1, B_1$) over a field F equivalent if invertible C and D exist over F such that $AC = DA_1$ and $BC = DB_1$). Unfortunately, I was only able to find the answer in the case if F is algebraically closed fields of characteristic 0.



If such a general theory exists (regardless of the field characteristic or whether it is algebraically closed or not), could you please point me to a source?



Thank you for your help.




matrices matrixpencil




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    I'm looking for a canonical form of pairs of matrices over arbitrary field up to equivalence (Calling pairs ($A, B$) and ($A_1, B_1$) over a field F equivalent if invertible C and D exist over F such that $AC = DA_1$ and $BC = DB_1$). Unfortunately, I was only able to find the answer in the case if F is algebraically closed fields of characteristic 0.



    If such a general theory exists (regardless of the field characteristic or whether it is algebraically closed or not), could you please point me to a source?



    Thank you for your help.




    matrices matrixpencil




    share|cite|improve this question























      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I'm looking for a canonical form of pairs of matrices over arbitrary field up to equivalence (Calling pairs ($A, B$) and ($A_1, B_1$) over a field F equivalent if invertible C and D exist over F such that $AC = DA_1$ and $BC = DB_1$). Unfortunately, I was only able to find the answer in the case if F is algebraically closed fields of characteristic 0.



      If such a general theory exists (regardless of the field characteristic or whether it is algebraically closed or not), could you please point me to a source?



      Thank you for your help.




      matrices matrixpencil




      share|cite|improve this question













      I'm looking for a canonical form of pairs of matrices over arbitrary field up to equivalence (Calling pairs ($A, B$) and ($A_1, B_1$) over a field F equivalent if invertible C and D exist over F such that $AC = DA_1$ and $BC = DB_1$). Unfortunately, I was only able to find the answer in the case if F is algebraically closed fields of characteristic 0.



      If such a general theory exists (regardless of the field characteristic or whether it is algebraically closed or not), could you please point me to a source?



      Thank you for your help.





      matrices matrixpencil





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 16 at 15:09







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      asked Jul 16 at 14:59









      UnrealVillager

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