tensor product of two column stochastic matrix [closed]












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Is the tensor product of two column/row stochastic matrix is again a column/row stochastic?
Thanks for helping.






matrices stochastic-matrices







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closed as off-topic by amWhy, user10354138, Markov, Brahadeesh, Henrik Nov 30 '18 at 14:32


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Brahadeesh, Henrik

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    0












    $begingroup$


    Is the tensor product of two column/row stochastic matrix is again a column/row stochastic?
    Thanks for helping.






    matrices stochastic-matrices







    share|cite|improve this question











    $endgroup$



    closed as off-topic by amWhy, user10354138, Markov, Brahadeesh, Henrik Nov 30 '18 at 14:32


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Brahadeesh, Henrik

    If this question can be reworded to fit the rules in the help center, please edit the question.



















      0












      0








      0





      $begingroup$


      Is the tensor product of two column/row stochastic matrix is again a column/row stochastic?
      Thanks for helping.






      matrices stochastic-matrices







      share|cite|improve this question











      $endgroup$




      Is the tensor product of two column/row stochastic matrix is again a column/row stochastic?
      Thanks for helping.






      matrices stochastic-matrices




      matrices stochastic-matrices






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 1 '18 at 17:31







      Markov

















      asked Nov 30 '18 at 11:44









      MarkovMarkov

      17.3k1059178




      17.3k1059178




      closed as off-topic by amWhy, user10354138, Markov, Brahadeesh, Henrik Nov 30 '18 at 14:32


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Brahadeesh, Henrik

      If this question can be reworded to fit the rules in the help center, please edit the question.







      closed as off-topic by amWhy, user10354138, Markov, Brahadeesh, Henrik Nov 30 '18 at 14:32


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Brahadeesh, Henrik

      If this question can be reworded to fit the rules in the help center, please edit the question.






















          1 Answer
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          $begingroup$

          The tensor product of two $ntimes n$ matrices $A,B$ is
          $$Aotimes B = left(begin{array}{ccc} a_{11}B & ldots& a_{1n}B\
          vdots & ldots & vdots\
          a_{n1}B & ldots & a_{nn} B
          end{array}right).$$
          So if $A,B$ are column stochastic, then so is $Aotimes B$. Just check the $j$-th column of the block matrix $Aotimes B$ and take inside the block matrix the $k$-th column of $B$:
          $$a_{1j}[b_{1k}+ldots+b_{nk}] + ldots + a_{nj}[b_{1k}+ldots+b_{nk}] = a_{1j}+ldots+a_{nj} = 1.$$
          Similar for the rows.






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            1 Answer
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            active

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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            The tensor product of two $ntimes n$ matrices $A,B$ is
            $$Aotimes B = left(begin{array}{ccc} a_{11}B & ldots& a_{1n}B\
            vdots & ldots & vdots\
            a_{n1}B & ldots & a_{nn} B
            end{array}right).$$
            So if $A,B$ are column stochastic, then so is $Aotimes B$. Just check the $j$-th column of the block matrix $Aotimes B$ and take inside the block matrix the $k$-th column of $B$:
            $$a_{1j}[b_{1k}+ldots+b_{nk}] + ldots + a_{nj}[b_{1k}+ldots+b_{nk}] = a_{1j}+ldots+a_{nj} = 1.$$
            Similar for the rows.






            share|cite|improve this answer









            $endgroup$


















              1












              $begingroup$

              The tensor product of two $ntimes n$ matrices $A,B$ is
              $$Aotimes B = left(begin{array}{ccc} a_{11}B & ldots& a_{1n}B\
              vdots & ldots & vdots\
              a_{n1}B & ldots & a_{nn} B
              end{array}right).$$
              So if $A,B$ are column stochastic, then so is $Aotimes B$. Just check the $j$-th column of the block matrix $Aotimes B$ and take inside the block matrix the $k$-th column of $B$:
              $$a_{1j}[b_{1k}+ldots+b_{nk}] + ldots + a_{nj}[b_{1k}+ldots+b_{nk}] = a_{1j}+ldots+a_{nj} = 1.$$
              Similar for the rows.






              share|cite|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                The tensor product of two $ntimes n$ matrices $A,B$ is
                $$Aotimes B = left(begin{array}{ccc} a_{11}B & ldots& a_{1n}B\
                vdots & ldots & vdots\
                a_{n1}B & ldots & a_{nn} B
                end{array}right).$$
                So if $A,B$ are column stochastic, then so is $Aotimes B$. Just check the $j$-th column of the block matrix $Aotimes B$ and take inside the block matrix the $k$-th column of $B$:
                $$a_{1j}[b_{1k}+ldots+b_{nk}] + ldots + a_{nj}[b_{1k}+ldots+b_{nk}] = a_{1j}+ldots+a_{nj} = 1.$$
                Similar for the rows.






                share|cite|improve this answer









                $endgroup$



                The tensor product of two $ntimes n$ matrices $A,B$ is
                $$Aotimes B = left(begin{array}{ccc} a_{11}B & ldots& a_{1n}B\
                vdots & ldots & vdots\
                a_{n1}B & ldots & a_{nn} B
                end{array}right).$$
                So if $A,B$ are column stochastic, then so is $Aotimes B$. Just check the $j$-th column of the block matrix $Aotimes B$ and take inside the block matrix the $k$-th column of $B$:
                $$a_{1j}[b_{1k}+ldots+b_{nk}] + ldots + a_{nj}[b_{1k}+ldots+b_{nk}] = a_{1j}+ldots+a_{nj} = 1.$$
                Similar for the rows.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Nov 30 '18 at 11:52









                WuestenfuxWuestenfux

                4,4981413




                4,4981413















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