- #1

twoski

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## Homework Statement

Determine constants c and C that do not depend on vector x but may depend on the dimension n of x, such that

[itex]c ||x||_{∞} ≤ ||x||_{1} ≤ C||x||_{∞}[/itex]

Use this result and the definition of matrix norms to find k and K that don't depend on the entries of matrix A (but depend on dimension n of A) such that

[itex]k ||A||_{∞} ≤ ||A||_{1} ≤ K||A||_{∞}[/itex]

## The Attempt at a Solution

Firstly i'm still trying to wrap my head around what an infinity norm actually is. According to my lecture notes,

[itex] ||x||_{∞} \equiv 1 ≤ k ≤ n, max|x_{k}|[/itex]

Does this mean the infinity norm is just the largest absolute value in x? There is no summation sign so my best guess is that "max" refers to the highest possible value contained in x.

So in other words i need to figure out constants which satisfy the inequality. My first guess would be to take c=0 and C=1, assuming that infinity norms are always greater than one-norms.