Is there a name of the rule that $ lVert x + z rVert^2 + lVert x - z rVert^2 = 2 lVert x rVert^2 + 2lVert z...
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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
edited 2 days ago
Asaf Karagila♦
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
$endgroup$
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
edited 2 days ago
Asaf Karagila♦
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
$endgroup$
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
edited 2 days ago
Asaf Karagila♦
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
$endgroup$
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
edited 2 days ago
Asaf Karagila♦
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
edited 2 days ago
Asaf Karagila♦
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
edited 2 days ago
Asaf Karagila♦
307k33438769
edited 2 days ago
Asaf Karagila♦
307k33438769
edited 2 days ago
Asaf Karagila♦
307k33438769
307k33438769
asked Mar 19 at 19:12
JaPJaP
203
asked Mar 19 at 19:12
JaPJaP
203
asked Mar 19 at 19:12
JaPJaP
203
203
add a comment |
add a comment |
1 Answer
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This is the parallelogram law of norms induced by inner products.
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
add a comment |
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1 Answer
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$begingroup$
This is the parallelogram law of norms induced by inner products.
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
add a comment |
$begingroup$
This is the parallelogram law of norms induced by inner products.
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
add a comment |
$begingroup$
This is the parallelogram law of norms induced by inner products.
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
$endgroup$
This is the parallelogram law of norms induced by inner products.
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
answered Mar 19 at 19:13
pulpfictionalpulpfictional
1986
1986
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
add a comment |
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
$begingroup$
Thank you so much!
$endgroup$
– JaP
Mar 19 at 19:32
add a comment |
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