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5. 低计算精度下实对称矩阵的特征值分解

低计算精度下实对称矩阵的特征值分解

来源 :高等学校计算数学学报 | 被引量 : 0次 | 上传用户：betterman_swp

【摘 要】

：

1引 言 rn1.1背景简介rn设A ∈Rn×n为n阶实对称矩阵,矩阵A的特征值分解是找正交矩阵U ∈Rn×n,使得rnA=UΛUT,(1.1)rn其中UT指U的转置,A为对角矩阵,且A=diag(λ1,λ2,...,λn),其中λi,i=1,...,n是矩阵A的特征值.矩阵A的奇异值分解为rnA=UΣUH,(1.2)rn其中,U ∈ Cn×n是酉矩阵,UH是U的共轭转置,Σ是非负实对角矩阵.当A正定时,奇异值分解和特征值分解等价.对一般实对称阵,奇异值和特征值绝对值相同.

【作 者】

：

胡乐宇 蔡邢菊 

【机 构】

：

南京师范大学数学科学学院,南京210023

【出 处】

：

高等学校计算数学学报

【发表日期】

：

2021年2期

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1引 言 rn1.1背景简介rn设A ∈Rn×n为n阶实对称矩阵,矩阵A的特征值分解是找正交矩阵U ∈Rn×n,使得rnA=UΛUT,(1.1)rn其中UT指U的转置,A为对角矩阵,且A=diag(λ1,λ2,...,λn),其中λi,i=1,...,n是矩阵A的特征值.矩阵A的奇异值分解为rnA=UΣUH,(1.2)rn其中,U ∈ Cn×n是酉矩阵,UH是U的共轭转置,Σ是非负实对角矩阵.当A正定时,奇异值分解和特征值分解等价.对一般实对称阵,奇异值和特征值绝对值相同.

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