Let V be a vector space over IF. Let T E L(V). Suppose P E L(V) is invertible. (a) Prove that T and P 'TP have the same eigenvalues. (Hint: TPP ' = TI = T.) (b) What is the relationship between the eigenvectors of T and the eigenvectos of P!TP?
Let V be a vector space over IF. Let T E L(V). Suppose P E L(V) is invertible. (a) Prove that T and P 'TP have the same eigenvalues. (Hint: TPP ' = TI = T.) (b) What is the relationship between the eigenvectors of T and the eigenvectos of P!TP?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let V be a vector space over F. Let T E L(V). Suppose P E L(V) is
invertible.
(a) Prove that T and P 'TP have the same eigenvalues. (Hint:
TPP 1=TI= T.)
(b) What is the relationship between the eigenvectors of T and the
eigenvectos of P 1TP?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e038964-a669-472d-8392-8724d2c97ab7%2Fcc2db252-4978-48d0-8785-e2f8b1b8532c%2F4v7ykj4_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a vector space over F. Let T E L(V). Suppose P E L(V) is
invertible.
(a) Prove that T and P 'TP have the same eigenvalues. (Hint:
TPP 1=TI= T.)
(b) What is the relationship between the eigenvectors of T and the
eigenvectos of P 1TP?
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