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
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Chapter2: Second-order Linear Odes
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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?
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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