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
SN - 0895-4798
VL - 23
SP - 517
EP - 523
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 2
ER -