Problem 5. The dual norm of || || on R" is defined as ||x|| = sup {x¹y | ||y|| ≤ 1, y ≤ R}. Prove that | || is a valid norm. (Hint: Try to show the essential properties of a norm including positive definiteness, positive homogeneity and triangle inequality.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
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Problem 5.
The dual norm of || || on Rn is defined as
||X||* = sup {xTy | ||y|| ≤ 1, y = R¹}.
Prove that | || is a valid norm. (Hint: Try to show the essential properties of a norm
including positive definiteness, positive homogeneity and triangle inequality.)
Transcribed Image Text:Problem 5. The dual norm of || || on Rn is defined as ||X||* = sup {xTy | ||y|| ≤ 1, y = R¹}. Prove that | || is a valid norm. (Hint: Try to show the essential properties of a norm including positive definiteness, positive homogeneity and triangle inequality.)
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