Endomorphism/Eigenvalue/Algebraic multiplicity/Definition

Algebraic multiplicity

Let

$\varphi \colon V\longrightarrow V$

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

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