hw1 - Homework 1 Foundations of Computational Math 1 Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 1 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesday, 9/8/09 Problem 1.1 This problem considers three basic vector norms: k . k 1 , k . k 2 , k . k . 1.1.a . Prove that k . k 1 is a vector norm. 1.1.b . Prove that k . k is a vector norm. 1.1.c. Consider k . k 2 . (i) Show that k . k 2 is definite. (ii) Show that k . k 2 is homogeneous. (iii) Show that for k . k 2 the triangle inequality follows from the Cauchy inequality | x H y | ≤ k x k 2 k y k 2 . (iv) Assume you have two vectors x and y such that k x k 2 = k y k 2 = 1 and x H y = | x H y | , prove the Cauchy inequality holds for x and y . (v) Assume you have two arbitrary vectors ˜ x and ˜ y . Show that there exists x and y that satisfy the conditions of part (iv ) and ˜ x = αx and ˜ y = βy where α and β are scalars. (vi) Show the Cauchy inequality holds for two arbitrary vectors ˜ x and ˜ y . Problem 1.2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.

Page1 / 2

hw1 - Homework 1 Foundations of Computational Math 1 Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online