TY - JOUR

T1 - The multiplicative inverse eigenvalue problem over an algebraically closed field

AU - Rosenthal, Joachim

AU - Wang, Xiaochang

PY - 2002

Y1 - 2002

N2 - Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Crossed Z sign be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Crossed Z sign such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Crossed Z sign is an affine variety over an algebraically closed field.

AB - Let M be an n × n square matrix and let p(λ) be a monic polynomial of degree n. Let Crossed Z sign be a set of n × n matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix Z ∈ Crossed Z sign such that the product matrix MZ has characteristic polynomial p(λ). In this paper we provide new necessary and sufficient conditions when Crossed Z sign is an affine variety over an algebraically closed field.

KW - Dominant morphism theorem

KW - Eigenvalue completion

KW - Inverse eigenvalue problems

UR - http://www.scopus.com/inward/record.url?scp=0036054827&partnerID=8YFLogxK

U2 - 10.1137/S0895479800378192

DO - 10.1137/S0895479800378192

M3 - Article

AN - SCOPUS:0036054827

VL - 23

SP - 517

EP - 523

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 2

ER -