Category:Eigenvalues of Linear Operators

This category contains results about eigenvalues in the context of Linear Operators.
Definitions specific to this category can be found in Definitions/Eigenvalues of Linear Operators.

Let $K$ be a field.

Let $V$ be a vector space over $K$.

Let $A : V \to V$ be a linear operator.

$\lambda \in K$ is an eigenvalue of $A$ if and only if:

$\map \ker {A - \lambda I} \ne \set {0_V}$

where:

$0_V$ is the zero vector of $V$

$I : V \to V$ is the identity mapping on $V$

$\map \ker {A - \lambda I}$ denotes the kernel of $A - \lambda I$.