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Name this simple norm equality! (Real Analysis)
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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.
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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?
real-analysis
asked 5 hours ago
JaPJaP
153
$endgroup$
add a comment |
$begingroup$
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
asked 5 hours ago
JaPJaP
153
$endgroup$
add a comment |
$begingroup$
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
asked 5 hours ago
JaPJaP
153
$endgroup$
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
asked 5 hours ago
JaPJaP
153
asked 5 hours ago
JaPJaP
153
asked 5 hours ago
JaPJaP
153
asked 5 hours ago
JaPJaP
153
asked 5 hours ago
JaPJaP
153
153
add a comment |
add a comment |
1 Answer
1
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This is the parallelogram law of norms induced by inner products.
answered 5 hours ago
pulpfictionalpulpfictional
1786
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
4 hours ago
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
This is the parallelogram law of norms induced by inner products.
answered 5 hours ago
pulpfictionalpulpfictional
1786
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
4 hours ago
add a comment |
$begingroup$
This is the parallelogram law of norms induced by inner products.
answered 5 hours ago
pulpfictionalpulpfictional
1786
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
4 hours ago
add a comment |
$begingroup$
This is the parallelogram law of norms induced by inner products.
answered 5 hours ago
pulpfictionalpulpfictional
1786
$endgroup$
This is the parallelogram law of norms induced by inner products.
answered 5 hours ago
pulpfictionalpulpfictional
1786
answered 5 hours ago
pulpfictionalpulpfictional
1786
answered 5 hours ago
pulpfictionalpulpfictional
1786
answered 5 hours ago
pulpfictionalpulpfictional
1786
1786
$begingroup$
Thank you so much!
$endgroup$
– JaP
4 hours ago
add a comment |
$begingroup$
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
add a comment |
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