symmetric representation of ternary forms associated to some toeplitz matrices †

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ID: 246172
2018
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Abstract
Let A be an n × n complex matrix. Assume the determinantal curve V A = { [ ( x , y , z ) ] ∈ CP 2 : F A ( x , y , z ) = det ( x ℜ ( A ) + y ℑ ( A ) + z I n ) = 0 } is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying F S ( x , y , z ) = F A ( x , y , z ) . It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of 4 × 4 nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from F A ( x , y , z ) associated to the specific 4 × 4 nilpotent Toeplitz matrices.
Reference Key
chien2018symmetrysymmetric Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Mao-Ting Chien, Hiroshi Nakazato
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Journal journal of hospitality and tourism management
Year 2018
DOI
10.3390/sym10030055
URL
http://www.mdpi.com/2073-8994/10/3/55
Keywords Keywords not found

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