Name this simple norm equality! (Real Analysis)












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I'm a bit new to real analysis. Today, I came across this particular equality, whcih seems obvious to me.
$$ lVert x + z rVert^2 + lVert x - z rVert^2 = 2 lVert x rVert^2 + 2lVert z rVert^2 $$
Is there a specific name for this?






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    1












    $begingroup$


    I'm a bit new to real analysis. Today, I came across this particular equality, whcih seems obvious to me.
    $$ lVert x + z rVert^2 + lVert x - z rVert^2 = 2 lVert x rVert^2 + 2lVert z rVert^2 $$
    Is there a specific name for this?






    real-analysis







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      I'm a bit new to real analysis. Today, I came across this particular equality, whcih seems obvious to me.
      $$ lVert x + z rVert^2 + lVert x - z rVert^2 = 2 lVert x rVert^2 + 2lVert z rVert^2 $$
      Is there a specific name for this?






      real-analysis







      share|cite|improve this question









      $endgroup$




      I'm a bit new to real analysis. Today, I came across this particular equality, whcih seems obvious to me.
      $$ lVert x + z rVert^2 + lVert x - z rVert^2 = 2 lVert x rVert^2 + 2lVert z rVert^2 $$
      Is there a specific name for this?






      real-analysis




      real-analysis






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      asked 5 hours ago









      JaPJaP

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      153






















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          This is the parallelogram law of norms induced by inner products.






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          • $begingroup$
            Thank you so much!
            $endgroup$
            – JaP
            4 hours ago











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          $begingroup$

          This is the parallelogram law of norms induced by inner products.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thank you so much!
            $endgroup$
            – JaP
            4 hours ago
















          6












          $begingroup$

          This is the parallelogram law of norms induced by inner products.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Thank you so much!
            $endgroup$
            – JaP
            4 hours ago














          6












          6








          6





          $begingroup$

          This is the parallelogram law of norms induced by inner products.






          share|cite|improve this answer









          $endgroup$



          This is the parallelogram law of norms induced by inner products.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 5 hours ago









          pulpfictionalpulpfictional

          1786




          1786












          • $begingroup$
            Thank you so much!
            $endgroup$
            – JaP
            4 hours ago


















          • $begingroup$
            Thank you so much!
            $endgroup$
            – JaP
            4 hours ago
















          $begingroup$
          Thank you so much!
          $endgroup$
          – JaP
          4 hours ago




          $begingroup$
          Thank you so much!
          $endgroup$
          – JaP
          4 hours ago


















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