特征值与特征向量?

2025-03-15 10:10:16
推荐回答(3个)
回答1:

1、属于不同特征值的特征向量一定线性无关。
2、相似矩阵有相同的特征多项式,因而有相同的特征值。
3、设x是矩阵a的属于特征值1的特征向量,且a~b,即存在满秩矩阵p使b=p(-1)ap,则y=p(-1)x是矩阵b的属于特征值1的特征向量。
4、n阶矩阵与对角矩阵相似的充分必要条件是:矩阵有n个线性无关的分别属于特征值1,2,3...的特征向量(1,2,3...中可以有相同的值)。
特征值是线性代数中的一个重要概念。在数学、物理学、化学、计算机等领域有着广泛的应用。设 A 是n阶方阵,如果存在数m和非零n维列向量 x,使得 Ax=mx 成立。

回答2:

这个问题太深沉了T^T

回答3:

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