Let be a norm on R n Prove that there is a constant C 0 such that the entries of every v ( 1 , 2 , , n ) T R n are all bounded, in absolute value, by i C v

Question: Let be a norm on R n . Prove that there is a constant C > 0 such that the entries of

Let ΙΙ · ΙΙ be a norm on Rⁿ. Prove that there is a constant C > 0 such that the entries of every v = (ν₁, ν₂, . . . , ν_n)^T ∈ Rⁿ are all bounded, in absolute value, by ΙΙ ν_iΙΙ ≤ C ΙΙ v ΙΙ.

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