Eigenvector
Also: eigenvectors, eigenvalue, eigenvalues
A nonzero vector v with Av = λv: applying the matrix A keeps v on its own line and scales it by the eigenvalue λ. Eigenvectors are the natural axes of a linear transformation.
A v = λ v
Example
A = [[3, 0], [0, 1]] stretches space 3× along x and leaves y alone, so (1, 0) is an eigenvector with λ = 3 and (0, 1) one with λ = 1.