The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

نویسندگان

Joachim Rosenthal

Xiaochang A. Wang

چکیده

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

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