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Name this simple norm equality! (Real Analysis)


Common Ground between Real Analysis and Measure TheoryReal analysis - proof approach helpReal analysis: simple second order ODEDoes this inequality involving the sum of components of a vector and its norm have a name?Why is this Inequality True for all Positive Real Numbers?What is real analysis?Is there a name for this set?Clarification on definition of a norm in a real analysis problemProb. 12, Sec. 5.2, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: Continuity of additive functionsReal Analysis: Not sure if textbook proof is incomplete.













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












    $begingroup$


    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






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 5 hours ago









      JaPJaP

      153




      153




















          1 Answer
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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










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          active

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          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












          $begingroup$

          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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