HW6 - MA/PH 607 Howell 10/3/2011 Homework Handout VI A. The...

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MA/PH 607 Howell 10/3/2011 Homework Handout VI A. The following all involve linear operators on a two-dimensional traditional vector space i with standard basis . Try to do all of these problems without refering to the U œ ß e f i j matrix for the operator. 1. What are all the eigenvalues and eigenvectors for the “magnification by 2” operator given by . ` # l r v v œ # 2. Consider the vector projection onto , pr , where . What is one a v a i j F l r a œ # m $ eigenvector corresponding to eigenvalue , and what is one eigenvector - œ " corresponding to eigenvalue ? (Hint: See example 7.1 in the notes.) - œ ! 3. Let be the rotation of every vector counterclockwise by a fixed angle Does e ) e ) ) Þ have any eigen-pairs if ? Why or why not? ! l l # ) 1 B. The following all involve linear operators on a three-dimensional traditional vector space i with standard basis . Try to do all of these problems without refering to the U œ ß ß e f i j k matrix for the operator. 1.
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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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HW6 - MA/PH 607 Howell 10/3/2011 Homework Handout VI A. The...

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