An eigenvector keeps its line of direction under a linear transformation. For this symmetric matrix, the directions and are perpendicular, with scale factors three and one.特征向量在线性变换后仍处于原来的直线上。对于这个对称矩阵， 与 两个方向相互垂直，对应伸缩倍数分别为三和一。
Gray spokes show the original unit circle. Green vectors along one diagonal stretch threefold; gold vectors along the other remain unchanged while intermediate directions turn.灰色辐条标出原单位圆。一条对角线上的绿色向量伸长为三倍，另一条上的金色向量保持不变，其间的一般方向则发生转动。