分析特征值及对应的特征向量

eigenvalues and eigenvectors are associated with square matrices. Given a square matrix A, it functions similarly to a linear transformation acting on the vector x, resulting in a new vector Ax. We are particularly interested in vectors that retain their direction when transformed by A. Mathematically, this relationship is expressed as Ax = λx, where λ represents the eigenvalue associated with the eigenvector x.

我们称λ为矩阵A的特征值，并且设x是矩阵A的一个特征向量。通常情况下，在讨论其属性时，“方向相同”常被用来指代它们指向同一方向；然而，在某些特定的情形下，“相反的方向”同样