Homework Help is Here – Start Your Trial Now!
Math
Algebra
or (Mt 0)

or (Mt 0)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 10AEXP
See similar textbooks
icon
Related questions
Question
100%
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.
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS