Hyperbolic polynomials and majorization

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PrGOW21-01.pdf (299.59 KB)

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http://www.math.umbc.edu/~gowda/tech-reports/PrGOW21-01.pdf

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http://hdl.handle.net/11603/26116

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UMBC Mathematics and Statistics Department
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https://orcid.org/0000-0001-5171-0924

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2021-10-14

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technical reports
preprints
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Abstract

On a finite dimensional real vector space V, we consider a real homogeneous polynomial p of degree n that is hyperbolic relative to a vector e ∈ V. This means that p(e) 6= 0 and for any (fixed) x ∈ V, the roots of the one-variable polynomial t 7→ p(te − x) are all real. Let λ(x) denote the vector in Rn whose entries are these real roots written in the decreasing order. Relative to the map λ : V → Rn, we introduce and study automorphisms, majorization, and doubly stochastic transformations