Endomorphism/Eigenvalue/Algebraic multiplicity/Definition

Let

${\displaystyle \varphi \colon V\longrightarrow V}$

be a linear mapping on a finite-dimensional ${\displaystyle {}K}$-vector space ${\displaystyle {}V}$, and ${\displaystyle {}\lambda \in K}$. The exponent of the linear polynomial ${\displaystyle {}X-\lambda }$ in the characteristic polynomial ${\displaystyle {}\chi _{\varphi }}$ is called the algebraic multiplicity of ${\displaystyle {}\lambda }$. It is denoted by

${\displaystyle {}\mu _{\lambda }=\mu _{\lambda }(\varphi )\,.}$