Definition:Eigenvalue/Real Square Matrix

Definition
Let $\mathbf A$ be a square matrix of order $n$ over $\R$.

Let $\lambda \in \R$.

$\lambda$ is an eigenvalue of $A$ if there exists a non-zero vector $\mathbf v \in \R^n$ such that:


 * $\mathbf A \mathbf v = \lambda \mathbf v$

Also see

 * Definition:Eigenvector of Real Square Matrix
 * Eigenvalues of Real Square Matrix are Roots of Characteristic Equation shows that we can find the eigenvalues of $\mathbf A$ by solving the equation $\map \det {\mathbf A - \lambda \mathbf I} = 0$ for $\lambda$.