Completing matrix $B$ so ${B=PA}$
$begingroup$
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.
matrices matrix-equations
asked Dec 21 '18 at 2:35
JulianJulian
1
$endgroup$
add a comment |
$begingroup$
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.
matrices matrix-equations
asked Dec 21 '18 at 2:35
JulianJulian
1
$endgroup$
add a comment |
$begingroup$
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.
matrices matrix-equations
asked Dec 21 '18 at 2:35
JulianJulian
1
$endgroup$
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
matrices matrix-equations
asked Dec 21 '18 at 2:35
JulianJulian
1
asked Dec 21 '18 at 2:35
JulianJulian
1
asked Dec 21 '18 at 2:35
JulianJulian
1
asked Dec 21 '18 at 2:35
JulianJulian
1
asked Dec 21 '18 at 2:35
JulianJulian
1
1
add a comment |
add a comment |
1 Answer
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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 $det(mathbf{P}) neq 0$
answered Dec 23 '18 at 20:29
ShewShew
596413
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1 Answer
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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 $det(mathbf{P}) neq 0$
answered Dec 23 '18 at 20:29
ShewShew
596413
$endgroup$
add a comment |
$begingroup$
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 $det(mathbf{P}) neq 0$
answered Dec 23 '18 at 20:29
ShewShew
596413
$endgroup$
add a comment |
$begingroup$
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 $det(mathbf{P}) neq 0$
answered Dec 23 '18 at 20:29
ShewShew
596413
$endgroup$
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 $det(mathbf{P}) neq 0$
answered Dec 23 '18 at 20:29
ShewShew
596413
answered Dec 23 '18 at 20:29
ShewShew
596413
answered Dec 23 '18 at 20:29
ShewShew
596413
answered Dec 23 '18 at 20:29
ShewShew
596413
596413
add a comment |
add a comment |
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