Re: Re: wrong answer or no answer?

*To*: mathgroup at smc.vnet.net*Subject*: [mg82867] Re: [mg82812] Re: wrong answer or no answer?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 1 Nov 2007 05:25:00 -0500 (EST)*References*: <200710291054.FAA06915@smc.vnet.net> <fg6pf3$ckv$1@smc.vnet.net> <200710311119.GAA22682@smc.vnet.net>

On 31 Oct 2007, at 20:19, Roger Bagula wrote: > Andrzej Kozlowski wrote: > >> Your matrix M has the property: >> >> MatrixPower[M, 2] >> {{0, 0}, {0, 0}} >> >> It is easy to prove using elementary linear algebra that such a >> matrix has no square root. In fact one can prove more. Suppose than M >> is an n by n matrix such that M^n=0 but M^(n-1) !=0 (in other words M >> is nilpotent of order n). Then M has no square root. >> >> The proof is easy so I won't bother to give it here. >> >> Andrzej Kozlowski >> >> >> >> > Andrzej Kozlowski > It certainly does have this property. > Your second post is probably best : > > If Det[M]=0, then MatrixPower[M,n]=0 not matter what n is. > This is completely false (and I did not write anything of the kind). M = {{0, 0, 0}, {1, 0, 0}, {1, 1, 0}} Det[M] 0 but MatrixPower[M, 2] {{0, 0, 0}, {0, 0, 0}, {1, 0, 0}} That is not the zero matrix. Andrzej Kozlowski