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- W2435160645 abstract "The problem of expressing a multivariate polynomial as the determinant of a monic (definite) symmetric or Hermitian linear matrix polynomial (LMP) has drawn a huge amount of attention due to its connection with optimization problems. In this paper we provide a necessary and sufficient condition for the existence of textit{monic Hermitian determinantal representation} as well as textit{monic symmetric determinantal representation} of size $2$ for a given quadratic polynomial. Further we propose a method to construct such a monic determinantal representtaion (MDR) of size $2$ if it exists. It is known that a quadratic polynomial $f(x)=x^{T}Ax+b^{T}x+1$ has a symmetric MDR of size $n+1$ if $A$ is textit{negative semidefinite}. We prove that if a quadratic polynomial $f(x)$ with $A$ which is not negative semidefinite has an MDR of size greater than $2$, then it has an MDR of size $2$ too. We also characterize quadratic polynomials which exhibit diagonal MDRs." @default.
- W2435160645 created "2016-06-24" @default.
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- W2435160645 date "2016-06-16" @default.
- W2435160645 modified "2023-09-26" @default.
- W2435160645 title "A Complete Characterization of Quadratic Polynomials that are determinants of Linear Matrix Polynomials" @default.
- W2435160645 hasPublicationYear "2016" @default.
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