Eigenvector centrality r. Consider the following figure. If the eigenvalue is negative, the eigenvector's direction is reversed. We do not consider the zero vector to be an eigenvector: since for every scalar the associated eigenvalue would be undefined. Eigenvectors are by definition nonzero. Eigenvectors are vectors that are not affected much by a transformation. For any square matrix A, a column vector v is said to be an eigenvector if Av = λv, where λ is the corresponding eigenvalue. . For any square matrix A of order n × n, the eigenvector is a column matrix of size n × 1. The example had λ = 0 : rows of A −0I in the direction (1,2); eigenvectorin the direction (2,−1) λ = 5 : rows of A −5I in the direction (−4,2); eigenvectorin the direction (2,4). In the figure, A, B, and C are points on a circle whose positions are determined by vectors a, b, and c respectively.