拟幂等矩阵的若干性质研究..doc

目 录 1 毕业论文任务书 ………………………………………… 1 2 毕业论文期中检查表 …………………………………….. 4 3 毕业论文开题报告 ……………………………………….. 5 4 毕业论文登记表 ………………………………………….. 8 5 毕业论文文稿 …………………………………………… Ⅰ 6 答辩许可证 ……………………………………………….. Ⅳ 7 毕业论文答辩记录 ……………………………………….. Ⅴ 拟幂等矩阵的若干性质研究 段刘刚 指导老师：王永兴 摘 要 幂等矩阵是高等代数矩阵论中相当重要的一类矩阵，它具有许多特殊性质，在矩阵论、数理统计理论及统计应用中有着广泛的应用.为进一步研究幂等矩阵、幂等变换、广义幂等矩阵、实幂等矩阵等，本文引入一个新的概念——拟幂等矩阵，它是对幂等矩阵的推广，并研究了拟幂等矩阵的分解、判别方法、对角化等问题，为求相关行列式的值、有关拟幂等矩阵秩的等式，提供有效的手段简化了论证，达到事半功倍的效果；特别是应用几种不同的方法，从不同的角度论证了判别一个矩阵是拟幂等矩阵的充要条件. 关键词 拟幂等矩阵；幂等矩阵；秩；向量空间；维数；迹 - Ⅰ - THE CERTAIN NATURE RESARCH OF QUASI-IDEMPOTENT MATRICES Duan Liu-gang Advisor: WanG Yong-xing (Department of Mathematics, Weinan Teachers College, Weinan 714000, Shaanxi) ABSTRACT The idempotent is a quite important kind of matrix in the advanced algebra theory of matrices, it has many special nature in the theory of matrices, and has the widespread application in the mathematical statistic theory and the statistical application,for further studies the idempotent, the idempotent transformation, the generalized idempotent, the solid idempotent and so on.This article introduces a new concept ---- quasi-idempotent matrices, it is to the idempotent promotion, and studied has quasi-idempotent matrices the decomposition, the distinction methods, the opposite angle and so on, at the solution of the value of correlation determinant, the related equalities of quasi-idempotent matrices rank , provided the effective method and simplified the proof, achieved the twice effects with half the effort; Specially, applies several different methods from the different angles to sufficiently wants of distinguishing a matrix was quasi-idempotent matrices . KE