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Finding minimum of sum of matrix elements


How to create a transition matrix that will guarantee an outcome after infinite transitionsFinding the inverse of a matrix by elementary transformations.Matrix of integers to boolean matrixApproximating a matrix so that 1) all rows sum to one and 2) all values have max 6 digits.$A$ has more columns than rows and has full row rank, show there exist infinitely many $B$ s.t. $AB=I$The geometry of a transformation given by a singular $2times 2$ matrix?Minimum Column/Row Matrix “Covering”2D standardization of a matrixDiscovering primary factors using matrix decompositionMatrix multiplication to reduce or increase certain elements of a matrix













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$begingroup$


Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?



For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.










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    0












    $begingroup$


    Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?



    For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.










    share|cite|improve this question









    New contributor




    flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$














      0












      0








      0





      $begingroup$


      Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?



      For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.










      share|cite|improve this question









      New contributor




      flute is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      Consider a 'row' which can be in one of $n$ states. I have an $n times n$ matrix $M$ such that $M(i,j)$ gives the interaction energy between a lower row in state $i$ and a row in state $j$ placed directly above it. I now want to stack infinitely many rows on top of each other in such a way that minimizes the total interaction energy. Is there a way to determine the sequence of states?



      For example, if there were only 4 stacked rows, in states 13, 71, 49 and 52, the total energy would be $M(13,71) + M(71,49) + M(49,52)$.







      matrices






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      share|cite|improve this question









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      edited 2 days ago







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      asked 2 days ago









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