查看“矩阵的频谱”的源代码

{{expert|time=2017-12-26T08:59:00+00:00}}
'''矩阵的频谱'''是一個[[數學]]術語，指一個[[矩阵]]的[[特徵值和特徵向量|特徵值]]的[[集合 (数学)|集合]]。<ref>{{harvtxt|Golub|Van Loan|1996|p=310}}</ref><ref>{{harvtxt|Kreyszig|1972|p=273}}</ref><ref>{{harvtxt|Nering|1970|p=270}}</ref>一般地，若<math>T\colon V\to V</math>是有限维向量空间<math>V</math>上的线性变换，则它的频谱为一系列标量<math>\lambda</math>的集合，满足矩阵<math>T-\lambda I</math>不可逆。矩阵特征值之积等于矩阵的[[行列式]]，而特征值之和等于矩阵的[[迹]]。<ref>{{harvtxt|Golub|Van Loan|1996|p=310|}}</ref><ref>{{harvtxt|Herstein|1964|pp=271–272}}</ref><ref>{{harvtxt|Nering|1970|pp=115–116}}</ref>

== 注释 ==
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== 参考文献 ==
* {{ citation | first1 = Gene H. | last1 = Golub | first2 = Charles F. | last2 = Van Loan | year = 1996 | isbn = 0-8018-5414-8 | title = Matrix Computations | edition = 3rd | publisher = [[Johns Hopkins University Press]] | location = Baltimore }}
* {{ citation | first1 = I. N. | last1 = Herstein | year = 1964 | isbn = 978-1114541016 | title = Topics In Algebra | publisher = [[Blaisdell Publishing Company]] | location = Waltham }}
* {{ citation | first1 = Erwin | last1 = Kreyszig | year = 1972 | isbn = 0-471-50728-8 | title = Advanced Engineering Mathematics | edition = 3rd | publisher = [[John Wiley & Sons|Wiley]] | location = New York }}
* {{ citation | first1 = Evar D. | last1 = Nering | year = 1970 | title = Linear Algebra and Matrix Theory | edition = 2nd | publisher = [[John Wiley & Sons|Wiley]] | location = New York | lccn = 76091646 }}

{{数学小作品}}

[[category:线性代数]]