Norm equalities and inequalities for three circulant operator matrices

Jiang, Zhao Lin; Qiao, Yun Cheng; Wang, Shudong

doi:10.1007/s10114-016-5607-z

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Theorem 31 If the Equality1

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2017

2023

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Cited by 5 publications

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“…where RSFPLRcircfc(T CUML ) is the row skew first-plus-last right circulant with the same first column as that of T CUML , and L(a i ) is the lower triangular Toeplitz matrix with the first column a i = (a i0 , a i1 , · · · , a i,n−1 ) T , and SCirc(b T i ) is the skew circulant matrix with the first row [17,19,22,33]. Theorem 3.2.…”

Section: Theorem 31 If the Equalitymentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are " similar" to the Toeplitz matrices. Their (−1, −1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (−1, 1)-circulants and (1, −1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.

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Section: Theorem 31 If the Equalitymentioning

confidence: 99%