The Multiplicity of Zeros of Algebraic System in Eigenvalue Method

摘要

This article deals with the structure relations between solutions to algebraic system and matrices in eigenvalue method for solving the algebraic system. The authors first discuss the condition on the ideal generated by the given system under which the eigenspace of matrix has dimension 1 since in this case the zero can be easily found. Then they study the relations between the multiplicity of zeros of the given system and orders of Jordan blocks of matrices formed in eigenvalue method.