Eigenvalue

An eigenvalue is a number that indicates how much a linear transformation stretches or compresses a vector that doesn’t change direction under that transformation (called an eigenvector). Mathematically, it satisfies ( A v = \lambda v ), where ( A ) is a square matrix, ( v ) is the eigenvector, and ( \lambda ) is the eigenvalue. In essence, it measures the scaling factor applied to certain special directions of a transformation.