20095ee103_1_hw1

20095ee103_1_hw1 - EIV Late homework will not be accepted...

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L. Vandenberghe EE103 Fall 2009 Homework 1 Due Thursday 10/1/09. 1. Exercise 1.4 in the course reader. 2. Exercise 1.5 in the course reader. 3. Exercise 1.7 in the course reader. 4. Exercise 1.10 in the course reader. 5. Use the Cauchy-Schwarz inequality to prove that 1 n n summationdisplay k =1 x k parenleftBigg 1 n n summationdisplay k =1 1 x k parenrightBigg - 1 for all n -vectors x with positive elements x k . The lefthand side of the inequality is the arithmetic mean (average) of the numbers x k ; the righthand side is called the harmonic mean. 6. Exercise 1.20 in the course reader. Homework instructions Homework will always be due by 5PM on the due date. A box for homework submis- sions will be placed on the file cabinet outside Prof. Vandenberghe’s office (66-147L
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Unformatted text preview: EIV). Late homework will not be accepted. • The Matlab ±les needed in some of the exercises (for example, exercise 1.20) can be found at www.ee.ucla.edu/ ~ vandenbe/ee103 The reader can be downloaded from the same address. • Make sure you use the Fall 2009 version of the course reader to ±nd the homework problems. Many of the exercises also appear in last year’s reader, but the numbering is sometimes di³erent. • You are allowed to work on the homework in small groups, but you must write up your own answers (and for programming assignments, write your own code) to hand in....
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