摘 要:正定矩阵是高等代数中一个重要的概念,矩阵奇异值分解是高等代数中一种重要的矩阵分解.本文主要探究两个问题.一是论证正定矩阵的几个定理,并结合二次型与矩阵合同的知识深入探讨正定矩阵.二是对奇异值分解的概念进行描述,并证明矩阵奇异值分解定理.最后利用一些例题来加深对正定矩阵与矩阵奇异值分解的理解.
关键词:正定矩阵;奇异值;矩阵分解8255
Positive Definite Matrix And Singular Value Decomposition
Abstract: Higher positive definite matrix algebra is an important concept, singular value decomposition is an important advanced algebra matrix factorization paper mainly explore two issues. First demonstration of several theorems positive definite matrix, combined with matrix quadratic depth knowledge of the contract definite matrix Second, the concept of singular value decomposition to describe and demonstrate matrix singular value decomposition theorem. Finally, some of the examples to deepen the positive definite matrix and singular value decomposition understanding.
Key words:Positive Definite Matrix; Singular Value ; Matrix Factorization
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