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0

$begingroup$

Suppose I have a square matrix $A$ (e.g., $ntimes n$) that multiplies some vector $y$ ($1times n$) into a vector of the same arrangement $z$ ($1times n$), such that $Ay = z$, where both $y$ and $z$ are known but not $A$. How many matrices can solve the equation, and how can I calculate that number?

matrix-equations

share|cite|improve this question

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If $bf y$ is the zero vector and $bf z$ is not, there are no solutions for $A$. Otherwise, there are infinitely many solutions. (Assuming we are dealing with real or complex matrices and vectors say).
  $endgroup$
  – Minus One-Twelfth
  Mar 19 at 23:33
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE! Please see math.meta.stackexchange.com/questions/5020/… for information on how to format expressions and equations on this site like I did in my edit to your question. It's not that hard to pick up!
  $endgroup$
  – Robert Howard
  Mar 19 at 23:44
  

  
  
  
  

add a comment | 

0

$begingroup$

Suppose I have a square matrix $A$ (e.g., $ntimes n$) that multiplies some vector $y$ ($1times n$) into a vector of the same arrangement $z$ ($1times n$), such that $Ay = z$, where both $y$ and $z$ are known but not $A$. How many matrices can solve the equation, and how can I calculate that number?

matrix-equations

share|cite|improve this question

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If $bf y$ is the zero vector and $bf z$ is not, there are no solutions for $A$. Otherwise, there are infinitely many solutions. (Assuming we are dealing with real or complex matrices and vectors say).
  $endgroup$
  – Minus One-Twelfth
  Mar 19 at 23:33
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to MSE! Please see math.meta.stackexchange.com/questions/5020/… for information on how to format expressions and equations on this site like I did in my edit to your question. It's not that hard to pick up!
  $endgroup$
  – Robert Howard
  Mar 19 at 23:44
  

  
  
  
  

add a comment | 

$begingroup$

Suppose I have a square matrix $A$ (e.g., $ntimes n$) that multiplies some vector $y$ ($1times n$) into a vector of the same arrangement $z$ ($1times n$), such that $Ay = z$, where both $y$ and $z$ are known but not $A$. How many matrices can solve the equation, and how can I calculate that number?

matrix-equations

share|cite|improve this question

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

$endgroup$

share|cite|improve this question

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

share|cite|improve this question

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

edited Mar 19 at 23:43

Robert Howard

2,3033935

edited Mar 19 at 23:43

Robert Howard

2,3033935

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32

asked Mar 19 at 23:30

Mathieu CharbonneauMathieu Charbonneau

32