Positive Definiteness of Arcsin of a Positve Definite Matrix [closed]












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Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?






linear-algebra normal-distribution positive-definite







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closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13


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    1












    $begingroup$


    Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?






    linear-algebra normal-distribution positive-definite







    share|cite|improve this question









    $endgroup$



    closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13


    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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas

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



















      1












      1








      1


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      $begingroup$


      Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?






      linear-algebra normal-distribution positive-definite







      share|cite|improve this question









      $endgroup$




      Suppose that $M$ is a positive definite matrix with entries within $[-1,1]$, and let $N$ be a matrix where $N_{ij} = sin^{-1}M_{ij}$. How do I show that $N$ is also positive definite?






      linear-algebra normal-distribution positive-definite




      linear-algebra normal-distribution positive-definite






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 27 at 21:51









      Sudeshna GargSudeshna Garg

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      closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13


      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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas

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







      closed as off-topic by max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas Jan 28 at 8:13


      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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – max_zorn, Cesareo, Gibbs, Lee David Chung Lin, onurcanbektas

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






















          1 Answer
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          $begingroup$

          This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.






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            1 Answer
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            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            2












            $begingroup$

            This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.






            share|cite|improve this answer











            $endgroup$


















              2












              $begingroup$

              This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.






              share|cite|improve this answer











              $endgroup$
















                2












                2








                2





                $begingroup$

                This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.






                share|cite|improve this answer











                $endgroup$



                This follows from the facts that the element-wise product of p.s.d. matrices is p.s.d, that the sum of p.s.d. matrices is p.s.d., and that the Taylor series for $arcsin$ has non-negative terms.







                share|cite|improve this answer














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                edited Jan 27 at 22:12

























                answered Jan 27 at 22:03









                kimchi loverkimchi lover

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                11.5k31229















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