Given A = 5 (a) Find all the eigenvalues and eigenvectors of A. Are the eigenvalues real? Are the eigenvectors orthogonal? (b) Is A symmetric? If so, is A positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite?
Given A = 5 (a) Find all the eigenvalues and eigenvectors of A. Are the eigenvalues real? Are the eigenvectors orthogonal? (b) Is A symmetric? If so, is A positive definite, positive semidefinite, negative definite, negative semidefinite, or indefinite?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 9RQ
Related questions
Question
parts a and b
![Given A =
5
(a) Find all the eigenvalues and eigenvectors of A. Are the eigenvalues real? Are the eigenvectors
orthogonal?
(b) Is A symmetric? If so, is A positive definite, positive semidefinite, negative definite, negative
semidefinite, or indefinite?
(c) What are the minimum and maximum values of the quadratic form ¹ Ar, when re R² satisfies
||||= 1 but can otherwise be arbitrarily chosen?
(d) Find the matrix norm ||A|| of A. What are the minimum and maximum gain input directions?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0698e99a-256c-4df5-818c-68ef08761670%2F90a17b07-ce9e-41c4-9a36-fbdb568f2f9c%2Fcc3uohb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given A =
5
(a) Find all the eigenvalues and eigenvectors of A. Are the eigenvalues real? Are the eigenvectors
orthogonal?
(b) Is A symmetric? If so, is A positive definite, positive semidefinite, negative definite, negative
semidefinite, or indefinite?
(c) What are the minimum and maximum values of the quadratic form ¹ Ar, when re R² satisfies
||||= 1 but can otherwise be arbitrarily chosen?
(d) Find the matrix norm ||A|| of A. What are the minimum and maximum gain input directions?
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