How to intuitively understand eigenvalue and eigenvector?

Intuition behind eigenvalues and eigenvectors. Mathstackexchange EigenMorality Punchlines from above links Eigenpairs are a lot like the roots of a polynomial. While roots of a polynomial ground the polynomial(fix its shape), eigenvalues limit the behavior of the linear transformation. The eigenvalues of a linear mapping is a measure of the distortion induced by the transformation and the eigenvectors tell you about how the distortion is oriented.