1. ## Doubt about Cayley-Hamilton theorem

Hi.

Can anybody tell me why he said that: "almost every square matrix satisfies his characteristic equation..."....why "almost", is it not true for every squared Matrix?:

Thanks.

2. ## Re: Doubt about Cayley-Hamilton theorem

I watched the entirety of the first clip. At the beginning he says "every square matrix satisfies its characteristic equation". Where does anyone say "almost every"?

3. ## Re: Doubt about Cayley-Hamilton theorem

Originally Posted by HallsofIvy
I watched the entirety of the first clip. At the beginning he says "every square matrix satisfies its characteristic equation". Where does anyone say "almost every"?
On the minute: 2:46 he say: "ALMOST every...", if you see the entire video he says this...

4. ## Re: Doubt about Cayley-Hamilton theorem

Thanks. Wikipedia says that the "Cayley-Hamilton theorem" is true "for every square matrix over a commutative ring. Of course the integers, rational numbers, and real numbers are "commutative rings" (the last two fields) so the "Cayley-Hamilton theorem" is true for any matrices whose entries are from our usual number systems.