Toeplitz matrices are unitarily similar to symmetric matrices. Issue 10 (3rd October 2017)

• Record Type: Journal Article
• Authors: Chien, Mao-Ting; Liu, Jianzhen; Nakazato, Hiroshi; Tam, Tin-Yau
• Is Part Of: Linear & multilinear algebra. Volume 65:Issue 10(2017)
• Page Start: 2131
• Page End: 2144
• Publication Date: 2017-10-03
• Subjects: Symmetric matrix -- Toeplitz matrix -- numerical range -- Kippenhahn polynomial; 15B05 -- 15A15 -- 15A60; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1330865
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : We prove that Toeplitz matrices are unitarily similar to complex symmetric matrices. Moreover, two unitary matrices that uniformly turn all Toeplitz matrices via similarity to complex symmetric matrices are explicitly given, respectively. When, we prove that each complex symmetric matrix is unitarily similar to some Toeplitz matrix, but the statement is false when .