Re: Characteristic polynomial - GL(3,2) matrices


"Robert Israel" <isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote
On Mar 21, 9:20 am, "boro.tti" <yesspammboro@tti> wrote:
"Robert Israel" <isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> ha scritto nel
messaggionews:rbisrael.20080321053938$46c6@xxxxxxxxxxxxxxxxxxx

"boro.tti" <yesspammboro@tti> writes:

Hi. Let M be a 3x3 matrix over Z_2. If M^3=1, how do we know that the
characteristic polynomial of M is x^3-1 ?

We don't. What if M is the identity matrix?

By the way... if M is the identity isn't that still true?

No, the characteristic polynomial of I is
(x-1)^3 = x^3 + x^2 + x + 1 (over Z_2).

Ok.


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