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The Construction of Solvents of Matrix Polynomials

Author: HaoQin
Tutor: LiSiZe
School: Beijing Jiaotong University
Course: Basic mathematics
Keywords: Matrix polynomial block companion matrix Eigen pair diagonalizable matrix roots of matrix polynomials
CLC: O151.21
Type: Master's thesis
Year: 2010
Downloads: 82
Quote: 0
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Abstract


In recent years, mathematicians for the roots of matrix polynomials with some research results, including the number of roots of matrix polynomial research, have obtained the number of roots of a matrix polynomial is infinite, or limited under what conditions. For the limited circumstance, they have estimated the minimum number and maximum root number.In this article, I further have studied the construction process of the roots of matrix polynomial, and got some new specific methods. The paper first introduces the basic theory of matrix polynomials and the issue that the roots of matrix polynomials are constructed by its Eigen pair and then describes the number problem of roots of matrix polynomials, and mainly explores how Eigen pairs which have been gotten forming roots of matrix polynomials are arranged, so as to arrive the root of the corresponding matrix polynomial.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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