“Jordan normal form”的概念、定义、习题解题方法及翻译-数学辞典

单词

Jordan normal form

释义

Jordan normal form

A block diagonal matrix where every block is a Jordan block. Every complex square matrix is similar to a matrix in Jordan normal form. The geometric multiplicity of an eigenvalue λ equals the number of Jordan blocks involving λ; the algebraic multiplicity of λ is the sum of those block's orders. The characteristic polynomial of the matrix is the product of all the block's characteristic polynomials; the minimal polynomial of the matrix is the product of the each eigenvalue's largest block's characteristic polynomials. Two such matrices are:

Both matrices have characteristic polynomials (x−1)2(x−2)4; the minimal polynomials are (x−1)(x−2)4 and (x−1)(x−2)2 respectively.

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