Conditions for $N_nX_nto O$, as $ntoinfty$

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Let, $X_n=((a^(n)_jk))_mtimes m$ be a sequence of matrices ($ngeq 1$), where $a^(n)_jk$ do not diverges to infinity (or negative infinity) as $ntoinfty$.



Let $N_n^mtimes m$ is a sequence of matrices ($ngeq 1$) with such that $N_nX_nto O$, as $ntoinfty$, where $O$ is null matrix.



What are the possible choices of $N_n$?




I was studying an example where $X_n$ is multiplied with $1/n$, from which I concluded that $N_n$ can be $textdiag(1/n,1/n,dots, 1/n)$. After thinking a little bit, I reduced the conditions to: $(j,k)$-th element of $N_n$, say $f_jk^(n)$ goes to $0$ as $ntoinfty$ or $f_jk^(n)=0$ after some $ngeq Min mathbbN$. Can we reduce (or generalize) the condition even more?




sequences-and-series matrices




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    Let, $X_n=((a^(n)_jk))_mtimes m$ be a sequence of matrices ($ngeq 1$), where $a^(n)_jk$ do not diverges to infinity (or negative infinity) as $ntoinfty$.



    Let $N_n^mtimes m$ is a sequence of matrices ($ngeq 1$) with such that $N_nX_nto O$, as $ntoinfty$, where $O$ is null matrix.



    What are the possible choices of $N_n$?




    I was studying an example where $X_n$ is multiplied with $1/n$, from which I concluded that $N_n$ can be $textdiag(1/n,1/n,dots, 1/n)$. After thinking a little bit, I reduced the conditions to: $(j,k)$-th element of $N_n$, say $f_jk^(n)$ goes to $0$ as $ntoinfty$ or $f_jk^(n)=0$ after some $ngeq Min mathbbN$. Can we reduce (or generalize) the condition even more?




    sequences-and-series matrices




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite












      Let, $X_n=((a^(n)_jk))_mtimes m$ be a sequence of matrices ($ngeq 1$), where $a^(n)_jk$ do not diverges to infinity (or negative infinity) as $ntoinfty$.



      Let $N_n^mtimes m$ is a sequence of matrices ($ngeq 1$) with such that $N_nX_nto O$, as $ntoinfty$, where $O$ is null matrix.



      What are the possible choices of $N_n$?




      I was studying an example where $X_n$ is multiplied with $1/n$, from which I concluded that $N_n$ can be $textdiag(1/n,1/n,dots, 1/n)$. After thinking a little bit, I reduced the conditions to: $(j,k)$-th element of $N_n$, say $f_jk^(n)$ goes to $0$ as $ntoinfty$ or $f_jk^(n)=0$ after some $ngeq Min mathbbN$. Can we reduce (or generalize) the condition even more?




      sequences-and-series matrices




      share|cite|improve this question












      Let, $X_n=((a^(n)_jk))_mtimes m$ be a sequence of matrices ($ngeq 1$), where $a^(n)_jk$ do not diverges to infinity (or negative infinity) as $ntoinfty$.



      Let $N_n^mtimes m$ is a sequence of matrices ($ngeq 1$) with such that $N_nX_nto O$, as $ntoinfty$, where $O$ is null matrix.



      What are the possible choices of $N_n$?




      I was studying an example where $X_n$ is multiplied with $1/n$, from which I concluded that $N_n$ can be $textdiag(1/n,1/n,dots, 1/n)$. After thinking a little bit, I reduced the conditions to: $(j,k)$-th element of $N_n$, say $f_jk^(n)$ goes to $0$ as $ntoinfty$ or $f_jk^(n)=0$ after some $ngeq Min mathbbN$. Can we reduce (or generalize) the condition even more?





      sequences-and-series matrices





      share|cite|improve this question










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