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Can you help me understand this statement:

An eigenvalue c has algebraic multiplicity $k$ if $(t-c)^k$ is the highest power of $(t-c)$ that divides the characteristic polynomial.

I am not sure, what does $t$ stand for. I have lifted this statement from the first statement under Algebraic Multiplicity heading from this link

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    @ArturoMagidin You're right, I misread it. Thanks.2012-06-17

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The algebraic multiplicity of an eigenvalue is its multiplicity as a root of the characteristic polynomial.

Then a root $c$ of $P(t)$ has multiplicity $\mu$ if $\mu$ is the highest integer such as $(t-c)^\mu$ divides $P(t)$.