Re: Nilpotent, Idempotent
- From: Timothy Murphy <tim@xxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 01 Dec 2006 23:04:03 +0000
G Patel wrote:
Some questions about nilpotenc/idempotence (hope those are words).
[A denotes nxn square matrix]
1) Can A^k = A for k > 2, while not for k=2, for some A ?
If A^3 = A then (squaring both sides) A^6 = A^2 but A^6 = A so A^2 = A.
2) Can A^k = 0 for k < n for some A ?
Certainly, eg if A = [0 0 1/0 0 0/0 0 0] then A^2 = 0.
Maybe I misunderstood the questions ...
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
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