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Suppose A is a symmetric matrix. (Au) = = ○ AUT Au OUTA ○ ATUT Suppose μ are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au) Tv = ○ Au Tv Ο μυν ☐ Au Tv (Check ALL that apply) Т u Tv , T Prove your result. Suggestion: If v are column vectors corresponding to the vectors u, v, then uv is a matrix whose entry is u · v. Explain why a symmetric matrix with real entries can't have complex eigenvalues. Suggestion: If A is a matrix with real entries and v is an eigenvector, then must also be an eigenvector. What is vv?

Suppose A is a symmetric matrix. (Au) = = ○ AUT Au OUTA ○ ATUT Suppose μ are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au) Tv = ○ Au Tv Ο μυν ☐ Au Tv (Check ALL that apply) Т u Tv , T Prove your result. Suggestion: If v are column vectors corresponding to the vectors u, v, then uv is a matrix whose entry is u · v. Explain why a symmetric matrix with real entries can't have complex eigenvalues. Suggestion: If A is a matrix with real entries and v is an eigenvector, then must also be an eigenvector. What is vv?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Suppose A is a symmetric matrix. (Au) = = ○ AUT Au OUTA ○ ATUT Suppose μ are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au) Tv = ○ Au Tv Ο μυν ☐ Au Tv (Check ALL that apply) Т u Tv , T Prove your result. Suggestion: If v are column vectors corresponding to the vectors u, v, then uv is a matrix whose entry is u · v.
Transcribed Image Text:Suppose A is a symmetric matrix. (Au) = = ○ AUT Au OUTA ○ ATUT Suppose μ are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au) Tv = ○ Au Tv Ο μυν ☐ Au Tv (Check ALL that apply) Т u Tv , T Prove your result. Suggestion: If v are column vectors corresponding to the vectors u, v, then uv is a matrix whose entry is u · v.
Explain why a symmetric matrix with real entries can't have complex eigenvalues. Suggestion: If A is a matrix with real entries and v is an eigenvector, then must also be an eigenvector. What is vv?
Transcribed Image Text:Explain why a symmetric matrix with real entries can't have complex eigenvalues. Suggestion: If A is a matrix with real entries and v is an eigenvector, then must also be an eigenvector. What is vv?
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