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Thread: Doubt about Cayley-Hamilton theorem

  1. #1
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    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.
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  2. #2
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    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"?
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  3. #3
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    Re: Doubt about Cayley-Hamilton theorem

    Quote Originally Posted by HallsofIvy View Post
    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...
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  4. #4
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    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.
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