首先, A的特征多项式f(x)=(x-a)(x-b).
若a不等于b, 则属于特征根x=a的一个特征向量为alpha=(1, 3). 属于特征根x=b的一个特征向量为beta=(0, 1).
若a=b, 则属于特征根x=a的两个线性无关特征向量可以取alpha=(1, 0)和beta=(0, 1) (此时任意非零向量都是特征向量).
Let f(x) be the characteristic polynomial of A. Then f(x)=(x-a)(x-b).
If a does not equal to b, then alpha=(1, 3) is an eigenvector associated to the eigenvalue a and beta=(0, 1) is an eigenvector associated to b.
If a=b, then every nonzero vector is an eigenvector of the eigenvalue a, and we can choose two linearly independent eigenvetors: alpha=(1, 0), beta=(0, 1).
