william_33
New member
- Joined
- Mar 4, 2013
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- 10
If f is a linear map on Rp→Rq, define ∣∣f∣∣pq=sup{∣∣f(x)∣∣∈Rp,∣∣x∣∣≤1}.
Show that the mapping f→∣∣f∣∣pq defines a norm on the vector space δ(Rp,Rq) of all linear functions on Rp→Rq. Show that ∣∣f(x)∣∣≤∣∣f∣∣pq∣∣x∣∣ for all x∈Rp.
I don't know how to prove this. Can anyone help me please?
Show that the mapping f→∣∣f∣∣pq defines a norm on the vector space δ(Rp,Rq) of all linear functions on Rp→Rq. Show that ∣∣f(x)∣∣≤∣∣f∣∣pq∣∣x∣∣ for all x∈Rp.
I don't know how to prove this. Can anyone help me please?