laqf07f_hw16 - 3 Section 6.3 Skip Application 2 3 4 Section...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Homework Assignment for Week 16 Assigned Dec 28, 2007 1. Section 6.1: Problems: 17, 18, 20, 27. Hint for Problem 18: Here | λ | denotes the length of the (possibly) complex eigenvalue λ . If λ = a + bi , i = - 1, then | λ | 2 = a 2 + b 2 = ( a + bi )( a - bi ) = λ ¯ λ . If x = x 1 . . . x n , then ¯ x = ¯ x 1 . . . ¯ x n . Show that ¯ x T x > 0 if x C n and x 6 = 0 . Next, show that if Q is a real matrix ( q ij R ) and Q x = λ x , then Q ¯ x = ¯ λ ¯ x . 2. Section 6.3: Read Application 1 up to the first half of the proof of Theorem 6.3.4. The second half of the proof of Theorem 6.3.4 and the paragraph that follows are beyond the scope of this course, thus the detail proofs are not provided.
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Unformatted text preview: 3. Section 6.3: Skip Application 2, 3. 4. Section 6.3: Problems: 1(b), 2(b), 3(b), 4, 7, 8(a,b), 9, 10 11, 14, 15, 16, 17, 19, 20, 23, 24(Hint: use Theorem 6.3.4), 31. 5. Section 6.3: I have decided to skip ”The Exponential of a Matrix” since most of you have not yet learned the series expansion of e x . For those who are interested in this part, here are some exercises for your practice: Problems 28, 29, 30. After reading this part and doing these exercises, you essentially will have learned about the materials in section 6.2. 1...
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This note was uploaded on 04/18/2010 for the course FINANCE 1231854365 taught by Professor Wuyiling during the Spring '10 term at Nashville State Community College.

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