Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897984 | Linear Algebra and its Applications | 2018 | 23 Pages |
Abstract
Let F(x,y,z) be a hyperbolic ternary form of degree n. The Helton-Vinnikov theorem asserts that there exists an nÃn complex symmetric matrix S such that FS(x,y,z)=F(x,y,z), where the determinantal hyperbolic ternary form of an nÃn matrix B is defined by FB(x,y,z)=detâ¡(xâ(B)+yâ(B)+zIn). Let A be an nÃn unitary bordering matrix. It is known that A is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity between the unitary bordering matrix A and the Helton-Vinnikov symmetric matrix S admitted the determinantal representation of the ternary form FA(x,y,z) satisfying FS(x,y,z)=FA(x,y,z) for n=3,4.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mao-Ting Chien, Hiroshi Nakazato,