I'm stuck to prove Nilpotent Matrix

by crazygrey
Tags: matrix, nilpotent, prove, stuck
crazygrey is offline
Oct17-06, 10:21 AM
P: 7
Hi all,
If a square matrix A of dimension n*n is a nilpotent matrix,i.e, A^k=0 for k>=m iff A has eigenvalues 0 with multiplicity n and index m or less. I did prove by induction if A^k=0 then all the eigenvalues are zero. I'm lost when I want to prove the oppesite, i.e, if all eigenvalues are zero then A^k=0? Please help
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
matt grime
matt grime is offline
Oct17-06, 12:02 PM
Sci Advisor
HW Helper
P: 9,398
Put it in jordan normal form and it all drops out. Alternatively just think about the characteristic poly.

Register to reply

Related Discussions
Nilpotent Matrix Proof Calculus & Beyond Homework 8
if A is nilpotent square matrix then I+A is invertibl Linear & Abstract Algebra 11
Matrix, Prove of matrix theorem Precalculus Mathematics Homework 4
Nilpotent matrix wit h index 2 Calculus & Beyond Homework 3
Nilpotent operators, matrix Calculus & Beyond Homework 2