Completing matrix $B$ so ${B=PA}$












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I have this problem.



${B=PA}$, where $P$ is a $ltimes l$ invertible unknown matrix. $A$,$B$ are two $l times m$ matrices.



All entries of A are known. Some entries of B are known, but some entries are missing. I want to complete these missed entries.



Theoretically, if $m$ is larger than $l$, we can find them by solving the linear equations. My questions is that are there other novel approaches to find these missed elements?



Thanks.










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    0












    $begingroup$


    I have this problem.



    ${B=PA}$, where $P$ is a $ltimes l$ invertible unknown matrix. $A$,$B$ are two $l times m$ matrices.



    All entries of A are known. Some entries of B are known, but some entries are missing. I want to complete these missed entries.



    Theoretically, if $m$ is larger than $l$, we can find them by solving the linear equations. My questions is that are there other novel approaches to find these missed elements?



    Thanks.










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I have this problem.



      ${B=PA}$, where $P$ is a $ltimes l$ invertible unknown matrix. $A$,$B$ are two $l times m$ matrices.



      All entries of A are known. Some entries of B are known, but some entries are missing. I want to complete these missed entries.



      Theoretically, if $m$ is larger than $l$, we can find them by solving the linear equations. My questions is that are there other novel approaches to find these missed elements?



      Thanks.










      share|cite|improve this question









      $endgroup$




      I have this problem.



      ${B=PA}$, where $P$ is a $ltimes l$ invertible unknown matrix. $A$,$B$ are two $l times m$ matrices.



      All entries of A are known. Some entries of B are known, but some entries are missing. I want to complete these missed entries.



      Theoretically, if $m$ is larger than $l$, we can find them by solving the linear equations. My questions is that are there other novel approaches to find these missed elements?



      Thanks.







      matrices matrix-equations






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      asked Dec 21 '18 at 2:35









      JulianJulian

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          since you know $mathbf{P}$, why cant you simply take the product of $mathbf{P}$ with $mathbf{A}$ and find the missing values in $mathbf{B}$ ?. If $mathbf{P}$ is unknown, best thing is to estimate $mathbf{P}$ using the known values in B using matrix factorization techniques. Since you want P to be invertible, you have to add extra constraints like $det(mathbf{P}) neq 0$






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            $begingroup$

            since you know $mathbf{P}$, why cant you simply take the product of $mathbf{P}$ with $mathbf{A}$ and find the missing values in $mathbf{B}$ ?. If $mathbf{P}$ is unknown, best thing is to estimate $mathbf{P}$ using the known values in B using matrix factorization techniques. Since you want P to be invertible, you have to add extra constraints like $det(mathbf{P}) neq 0$






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              since you know $mathbf{P}$, why cant you simply take the product of $mathbf{P}$ with $mathbf{A}$ and find the missing values in $mathbf{B}$ ?. If $mathbf{P}$ is unknown, best thing is to estimate $mathbf{P}$ using the known values in B using matrix factorization techniques. Since you want P to be invertible, you have to add extra constraints like $det(mathbf{P}) neq 0$






              share|cite|improve this answer









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                0





                $begingroup$

                since you know $mathbf{P}$, why cant you simply take the product of $mathbf{P}$ with $mathbf{A}$ and find the missing values in $mathbf{B}$ ?. If $mathbf{P}$ is unknown, best thing is to estimate $mathbf{P}$ using the known values in B using matrix factorization techniques. Since you want P to be invertible, you have to add extra constraints like $det(mathbf{P}) neq 0$






                share|cite|improve this answer









                $endgroup$



                since you know $mathbf{P}$, why cant you simply take the product of $mathbf{P}$ with $mathbf{A}$ and find the missing values in $mathbf{B}$ ?. If $mathbf{P}$ is unknown, best thing is to estimate $mathbf{P}$ using the known values in B using matrix factorization techniques. Since you want P to be invertible, you have to add extra constraints like $det(mathbf{P}) neq 0$







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 23 '18 at 20:29









                ShewShew

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