An eigenvalue, often denoted with $λ$, is a scalar value which indicates how much an eigenvector is scaled when a matrix acts on it. They are sometimes also known as “characteristic values”.

Eigenvalue-eigenvector problems are usually illustrated by the equation: $Ax=λx$

- A is a square matrix
- x is an eigenvector
- $λ$ is an eigenvalue

$AX= 000 522−9 −1016−2 × −5−43 $ $AX= −50−4030 =10 −5−43 $Example

In the problem above, we can see that the eigenvalue is $λ=10$ for the matrix A.

We may also see that $ −5−43 $ is the eigenvector.

# Characteristic Equation

To find eigenvalues, you solve the characteristic equation:

$det(A−λI=0)$Where $A$ is the given matrix, $λ$ is the eigenvalue, and $I$ is the identity matrix of the same size as $A$.