STATS 231
Stanford University
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Stanford UniversitySTATS 231hw0-solutions
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--210July 20212020/2021A+
- Homework 0 solutions 
CS229T/STATS231 
1. Linear algebra (0 points) 
a (dual norm of L1 norm) The L1 norm k · k1 of a vector v 2 Rn is defined as 
kvk1 = 
nX i 
=1 
jvij: (1) 
The dual norm k · k∗ of a norm k · k is defined as 
kvk∗ = sup 
kwk≤1 
(v · w): (2) 
Compute the dual norm of the L1 norm. (Here v · w denotes the inner product between v and w: v · w , 
Pn i=1 viwi) 
Solution: 
We will prove that 
sup 
kwk1≤1 
(v · w) = max 
i2[n] 
vi = kvk1 (3) 
which implies that the dua...
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