Characteristic Polynomial and Multiplicity

What is the characteristic polynomial

• IT IS

  • $\det (A-\lambda I)$

What is algebraic multiplicity

• Let ${\lambda }_i$ be an eigen value of A.

  • the algebraic multiplicity of ${\lambda }_i$ is the number of times the factor of $\lambda -{\lambda }_i$ shows up in the factored formo f the characteristic polynomial