Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk +..+ ast + ao be a polynomial such that p(A) akAk + ...+ a, A+ aoI = 0. = 0 for all eigenvalues A of A. Show that p(A) %3!
Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk +..+ ast + ao be a polynomial such that p(A) akAk + ...+ a, A+ aoI = 0. = 0 for all eigenvalues A of A. Show that p(A) %3!
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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Transcribed Image Text:Problem 1. Let A E Mn(F) be diagonalizable, and let p(t) = artk + ...+ art + ao
be a polynomial such that p() = 0 for all eigenvalues A of A. Show that p(A)
ak Ak + ...+ a, A+ aoI = 0.
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