可逆矩阵及其简单应用.docx

可逆矩阵及其简单应用

第一篇：可逆矩阵及其简单应用石家庄学院毕业设计（论文）它的系数矩阵和增广矩阵的性质上，并且解方程组的过程也表现为变换这些矩阵的过程。可逆矩阵作为矩阵乘法的逆运算,是矩阵的一种重要运算,在解决矩阵问题中起着重要的作用。因而掌握可逆矩阵的求法,在解决实际问题时,往往可以起到事半功倍的效果。本文将对一些常用的可逆矩阵的求法作系统的总结，并进一步介绍几种常见得可逆矩阵的在数学领域和通讯领域的简单应用。【关键词】矩阵可逆矩阵通信【Abstract】Inthediscussionoflinearequations,wecanseethatsome可逆矩阵及其简单应用importantpropertiesofthelinearequationsarereflectedinitscoefficientmatrixandaugmentedmatrixofnature,what`smore,theprocessofthesolutionperformanceoftheprocessoftransformationofthesematrices.Invertiblematrixmultiplicationastheinverseofthematrixisanimportantmatrixoperations,andplaysanimportantroleinsolvingtheproblem.masterringthemethodofInvertiblematrixoftencanplayamultipliereffectinsolvingpracticalproblems.ThefollowingarethesystemsummaryofthecommonlyusedreversiblemethodfortheevaluationofInvertiblematrix,andfurtherdescripitionsofseveralcommonapplicationinthefieldofmathematicsandsimplecommunications.【KeyWords】MatrixInvertiblematrixCommunications石家庄学院毕业设计（论文）目录前言...................................................................5一、可逆矩阵...........................................................5二、可逆矩阵的性质及求法...............................................5（一）性质..............................................................5（二）逆矩阵求法.........................................................6三、可逆矩阵的简单应用.................................................10（一）可逆矩阵在数学方面的应用............................................10（二）可逆矩阵在通信方面的应用.........................................11（1）加密保密通信模型.......................................................12（2）可逆矩阵的应用........................................................12（3）加密密钥的生成........................................................13（4）解密密钥的生成........................................................14（5）明文矩阵的选择........................................................14（6）加密矩阵的选择........................................................14（7）算法优化............................................................14结论......................................................