What would you like to understand?

A nonzero vector $v$ is an eigenvector of a matrix $A$ when the matrix-vector product $Av$ equals a scalar multiple of $v$, written as $Av = \lambda v$. The scalar $\lambda$ is the corresponding eigenvalue.

Conditions: $v$ must be a nonzero vector.; $A$ is a square matrix.; $\lambda$ is a scalar.

A nonzero vector $v$ is an eigenvector of a matrix $A$ when the matrix-vector product $Av$ equals a scalar multiple of $v$, written as $Av = \lambda v$. The scalar $\lambda$ is the corresponding eigenvalue.

Conditions: $v$ must be a nonzero vector.; $A$ is a square matrix.; $\lambda$ is a scalar.