关于（斜）对合矩阵和（斜）二次卷积矩阵的奇异值分解

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-05-27 DOI:10.1515/spma-2020-0001

H. Faßbender, Martin Halwass

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引用次数: 0

摘要

摘要n×n对合矩阵A的奇异值σ>1成对出现（σ，1σ｛1\over\sigma｝）。它们的左奇异向量和右奇异向量是紧密相连的。详细讨论了奇异值σ=1的情况。这些奇异值可以与紧密连接的左右奇异向量成对出现（1，1），也可以单独出现。利用左右奇异向量之间的联系，将对合矩阵的奇异值分解（SVD）重新表述为本征分解。这显示了对合矩阵的奇异值与其特征值之间有趣的关系。类似的观察结果适用于SVD、（斜）二次卷积矩阵的奇异值和共轭值。

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On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices

Abstract The singular values σ > 1 of an n × n involutory matrix A appear in pairs (σ, 1σ {1 \over \sigma } ). Their left and right singular vectors are closely connected. The case of singular values σ = 1 is discussed in detail. These singular values may appear in pairs (1,1) with closely connected left and right singular vectors or by themselves. The link between the left and right singular vectors is used to reformulate the singular value decomposition (SVD) of an involutory matrix as an eigendecomposition. This displays an interesting relation between the singular values of an involutory matrix and its eigenvalues. Similar observations hold for the SVD, the singular values and the coneigenvalues of (skew-)coninvolutory matrices.

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.