  We investigate eigenvectors of rank-one deformations of random matrices
$\boldsymbol B = \boldsymbol A + \theta \boldsymbol {uu}^*$ in which
$\boldsymbol A \in \mathbb R^{N \times N}$ is a Wigner real symmetric random
matrix, $\theta \in \mathbb R^+$, and $\boldsymbol u$ is uniformly distributed
on the unit sphere. It is well known that for $\theta > 1$ the eigenvector
associated with the largest eigenvalue of $\boldsymbol B$ closely estimates
$\boldsymbol u$ asymptotically, while for $\theta < 1$ the eigenvectors of
$\boldsymbol B$ are uninformative about $\boldsymbol u$. We examine $\mathcal
O(\frac{1}{N})$ correlation of eigenvectors with $\boldsymbol u$ before phase
transition and show that eigenvectors with larger eigenvalue exhibit stronger
alignment with deforming vector through an explicit inverse law. This
distribution function will be shown to be the ordinary generating function of
Chebyshev polynomials of second kind. These polynomials form an orthogonal set
with respect to the semicircle weighting function. This law is an increasing
function in the support of semicircle law for eigenvalues $(-2\: ,+2)$.
Therefore, most of energy of the unknown deforming vector is concentrated in a
$cN$-dimensional ($c<1$) known subspace of $\boldsymbol B$. We use a
combinatorial approach to prove the result.
