Eigenvalue is important knowledge points in linear algebra,serving as the foundation for matrix diagonal-ization and standardization of the quadratic form,and have significant applications in theory and practice in many fields.The eigenvalue calculation of an n-order square matrix involves two steps:solving the characteristic polyno-mial|A-λE|and the characteristic equation|A-λE|=0.Solving characteristic polynomial is equivalent to solving an n-order determinant containing variables,while solving characteristic equations is equivalent to solving an one dimension equation of the n-degree,which is generally computationally cumbersome.Using several examples to demonstrate the calculation of eigenvalues.Firstly,the basic method of eigenvalue calculation is discussed,and then several techniques for eigenvalue calculation with special matrices are provided.At the same time,to apply these computational techniques,proficiency in the properties of determinants,matrices,eigenvalues and eigenvectors is re-quired,the particularities of solving characteristic polynomials and equations can be perceived,so as to obtain eigen-values concisely and accurately.
关键词
特征值/特征多项式/因式分解/矩阵的迹/矩阵的秩
Key words
Eigenvalue/Characteristic polynomial/Factorization/Trace of matrix/Rank of matrix
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