Prove there exists a positive number c such that two inner products with corresponding norms?
1 answer:
Answer:
See explanation below
Step-by-step explanation:
We assume that we have two inner products
on v such that
if and only if
and we want to proof is there is a positive number c like this :
for every
in V
We can assumee that we have an orthonormal basis
of V with respect
. We can define the following sets:
both defined on a n dimensional space, and then we have that for any linear comibnation we have this:

And A neds to be a matrix with entries 
So then we have this:

And then we have the maximum defined and we need to satisfy that c is the maximum value for te condition required.
for every
in V
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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