Hi,

one of my books states the inequality as

for all ,

and says thatequalityholds if and only if for

.

To me it looks like equality holds if for any :

I do not understand why it has to be .

Could someone please clear it up a bit? Thanks.

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- February 9th 2011, 12:49 AMMollierCauchy-Schwarz inequality
Hi,

one of my books states the inequality as

for all ,

and says that*equality*holds if and only if for

.

To me it looks like equality holds if for any :

I do not understand why it has to be .

Could someone please clear it up a bit? Thanks. - February 9th 2011, 01:36 AMFernandoRevilla
The result is the following:

You have proven .

To prove you'll need to choose a particular .

Fernando Revilla - February 9th 2011, 03:04 AMMollier
- February 9th 2011, 05:25 AMFernandoRevilla

If the equality is trivial and is linearly dependent . If decompose:

Using , prove that and .

That is or equivalently being .

Fernando Revilla