An eigenvector is a special, non-zero vector whose direction does not change when a linear transformation (matrix) is applied to it. An eigenvalue is the scalar factor by which that eigenvector is scaled (stretched, compressed, or flipped) during the transformation.

An eigenvector is a special, non-zero vector whose direction does not change when a linear transformation (matrix) is applied to it. An eigenvalue is the scalar factor by which that eigenvector is scaled (stretched, compressed, or flipped) during the transformation. 

Together, they satisfy the equation:

Av = λ v

Where A is the matrix, v is the eigenvector, and λ (lambda) is the eigenvalue.