What is "eigenvector"

n. 1 (context linear algebra English) A vector that is not rotated under a given linear transformation; a left eigenvector or right eigenvector depending on context. 2 (context physics engineering English) A right eigenvector; a nonzero vector $x$ such that, for a particular matrix $A$, $A\; x\; =\; lambda\; x$ for some scalar $lambda$ which is its eigenvalue and an eigenvalue of the matrix.