This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 580 / Math 587 SPRING 2011 Correspondence # 1 January 24, 2011 ASSIGNMENT 1 Reading Assignment: Text: Chapters 1 & 2. Recommended Reading: Curtain & Pritchard: Chapter 1. Problems (to be handed in): Due Date: Thursday, February 3 . 1. Let M and N be subspaces in a vector space. Show that [ M N ] = M + N , where the set operations [ ] and + are as defined in the text (also introduced in class). [This is Problem 3 on page 43 of the text.] 2. A convex combination of the vectors x 1 ,x 2 ,...,x n is a linear combination of the form x 1 + 2 x 2 + + n x n where i 0 for each i , and 1 + 2 + + n = 1. Given a set S in a vector space, let K be the set of vectors consisting of all convex combinations from S . Show that K = co(S), where co( ) is defined on p. 18 of the text. [This is Problem 4 on page 43 of the text.] 3. Obtain a continuous function x ( ) on the interval [ 1 , 1] which maximizes the integral 1 1 t 3 x ( t )...
View
Full
Document
 Spring '08
 Staff

Click to edit the document details