摘 要:本文给出了矩阵之和的特征值与奇异值同原矩阵的特征值与奇异值之间的大小关系,以及矩阵之和的特征值与奇异值的求法.首先通过矩阵之和特征值及奇异值的定义,给出了矩阵之和存在特征值和奇异值的条件;其次给出矩阵之和特征值与奇异值的性质,即是其与原矩阵特征值与奇异值之间的不等式关系;再次给出了矩阵之和特征值的求法,及奇异值的求法.38158 毕业论文关键词: 特征值; 特征向量; 奇异值; 矩阵之和
Eigenvalue and Singular Value from the Sum of Matrices
Abstract: In this article, through understanding of eigenvalue and singular value, I give the conclusion that the relationship between the eigenvalue and singular value from the sum of matrices and original’s, and how to calculate the eigenvalue and singular value from the sum of matrices. First of all, through the definition of the eigenvalue and singular value from the sum of matrices, I give the existence conditions of the eigenvalue and singular value from the sum of matrices. Secondly, on the basis of others research, I give the nature of eigenvalue and singular value from the sum of matrices which is the inequality relation of between the eigenvalue and singular value from the sum of matrices and original’s. The last, I give the solution method of the eigenvalue and singular value from the sum of matrices.
Key Words: Eigenvalue; Eigenvectors; Singular value; the sum of matrices
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