HW3 - and be so that + , # $ ± ²3 + , ” • 1. 2. is...

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MA/PH 607 9/9/2011 Homework Handout III A. Read § 4.1 in the online notes, doing any in-notes exercises. Also skim/read §3.2 of A&W (Arfken & Weber), at the starting with Basic Definitions bottom of page 177. read about the stuff on “direct products” and “trace” even though we won’t do much with them). Starting on page 187 of A&W, “be sure you can do” # 1, 2 (note: is the c d A B AB BA ß œ “commutator” for AB may also be interesting — look at them, at least). B. Compute where , and then find some nonzero matrices A A # œ # ‚ # α " # $ satisfying . A 0 # œ C. Find the conjugate, the transpose, and the adjoint for each of the following matrices: A B C œ œ œ "3 #3 $ # ± $3 ²3 $3 3 ) # ± $3 ( ± )3 Ô × Õ Ø , , D. What should
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Unformatted text preview: and be so that + , # $ ± ²3 + , ” • 1. 2. is symmetric? is Hermitian (i.e., self adjoint)? E. Give an example of a anti-Hermitian matrix with no zero entries. # ‚ # F. Do NOT read §3.3 or §3.4 of A&W, but, starting on page 212, do 4, 5 and 6. G. Let and (assume the basis is orthonormal). Compute the l Ù œ l Ù œ + @ + @ + @ a v Ô × Ô × Õ Ø Õ Ø " " # # $ $ following (remember, scalars are complex) and, if possible, compare each with : Ø l Ù a v 1. 2. 3. trace Ø l Œ l Ù l Ù Œ Ø l Ø l Œ l Ù a v v a a v & ± Read § 4. and § 4.4 in the notes, doing any in-text or in-H. $ Elementary Matrix Theory lecture exercises. Also skim §3.1 of A&W. Starting on page 174 of A&W, do # 1 and 2 (rewrite the system in “matrix/vector form” first, and think about what the problem is really about). Then do #6b on page 188....
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This note was uploaded on 11/07/2011 for the course MA 607 taught by Professor Staff during the Summer '11 term at University of Alabama in Huntsville.

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