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矩阵的特征值和特征向量是矩阵与变换的一个非常重要的内容,利用矩阵的特征值和特征向量,可以方便地计算多次矩阵变换的结果,而且在实际工程计算和工程控制中也发挥着重要作用.二阶矩阵的特征值和特征向量有两个基本内容.一是二阶矩阵的特征值和特征向量的概念:设A是一个二阶矩阵,如果对于实数λ,存在一个非零向量α,使得Aα=λα,那么λ称为A的一个特征值,而α称为A的属于特征值λ的一个特征向量.
The eigenvalues and eigenvectors of matrices are a very important part of matrices and transformations. The eigenvalues and eigenvectors of matrices make it easy to calculate the result of multiple matrix transformations, and also play an important role in practical engineering calculation and engineering control One is the concept of eigenvalues and eigenvectors of second-order matrices: Let A be a second-order matrix, and if there exists a nonzero vector for the real number λ α such that Aα = λα, then λ is called a characteristic value of A, and α is called a characteristic vector of A belonging to eigenvalue λ.