or (Mt 0)

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 that N, an operator on C, is nilpotent: Nk = 0, but N-10.
a) Show that if A is an eigenvalue of N, then A= 0.
b) What are the characteristic (g(z)) and minimal (p(z)) polynomials of N?
c) If M is another nilpotent operator (Mt = 0) that commutes with N (MN = NM), P
N+M is also nilpotent.
Transcribed Image Text:Suppose that N, an operator on C, is nilpotent: Nk = 0, but N-10. a) Show that if A is an eigenvalue of N, then A= 0. b) What are the characteristic (g(z)) and minimal (p(z)) polynomials of N? c) If M is another nilpotent operator (Mt = 0) that commutes with N (MN = NM), P N+M is also nilpotent.
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