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Machine Learning
book

Machine Learning

by Sergios Theodoridis
April 2015
Intermediate to advanced content levelIntermediate to advanced
1062 pages
40h 35m
English
Academic Press
Content preview from Machine Learning

Problems

9.1 If xi,yi, i = 1,2,…,l, are real numbers, then prove the Cauchy-Schwarz inequality:

i=1lxiyi2i=1lxi2i=1lyi2.

si142_e

9.2 Prove that the 2 (Euclidean) norm is a true norm, that is, it satisfies the four conditions that define a norm.

Hint

To prove the triangle inequality, use the Cauchy-Schwarz inequality.

9.3 Prove that any function that is a norm is also a convex function.

9.4 Show Young’s inequality for nonnegative real numbers a and b,

abapp+bqq,

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for >p>1 and >q>1 such that

1p+1q=1.

9.5 Prove Holder’s inequality for

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Publisher Resources

ISBN: 9780128015223