线性代数论文

经典word整理文档，仅参考，双击此处可删除页眉页脚。本资料属于网络整理，如有侵权，请联系删除，谢谢！[]线性代数论文题目：行列式的性质学院：计算机科学与技术学院班级：2013级网络工程本四姓名：指导教师：职称：完成日期：2014年10月30日摘要：通过学习n阶行列式的定义，我们知道了n阶行列式共有n！项，所以直接用定义来计算n阶行列式的计算量相当大，即使是用目前最快的计算机也很难实现。如果用定义计算一个25阶行列式，需做超过251.5*1025次的乘法运算，若一个超级计算机每秒钟能够完成1万亿次乘法运算。用这种方法计算一个25阶行列式，也将需要运算50万年。因此如何快速的计算行列式是我们急需解决的问题，为此，我们先来研究行列式的性质。关键词：行列式；行列式的性质；计算Abstract：Throughthedefinitionoflearningnorderdeterminant,weknowtherearennorderdeterminant!Acalculationdirectly,sotocalculatethenorderdeterminantdefinitionisquitelarge,evenifitisalsoverydifficulttoachievebyfarthefastestcomputer.Ifthecalculationofa25orderdeterminantbydefinition,needtodomorethan25!Aboutmultiplicationof1.5*1025times,ifasupercomputertocomplete1trilliontimespersecondmultiplication.Thecalculationofa25orderdeterminantinthisway,willalsoneedtobeoperationalin500000years.Therefore,tocomputethedeterminantofhowfastweneedtosolvetheproblems,therefore,wefirststudythepropertiesofdeterminant.Keywords：determinant;determinantproperty;calculation第1页目录1.1引言.................................................................................................................................11.1.1性质1.....................................................................................................................................2例题.............................................................................................................................................31.1.2性质2.....................................................................................................................................2例题.............................................................................................................................................31.1.3性质3.....................................................................................................................................2例题.............................................................................................................................................31.1.4性质4.....................................................................................................................................2例题.............................................................................................................................................31.1.5性质5.....................................................................................................................................2例题.............................................................................................................................................31.1.6性质6.....................................................................................................................................2例题.............................................................................................................................................31.1.7性质7.....................................................................................................................................2例题.............................................................................................................................................3第2页1.1引言设：aaaaaaaaann1aaaD,D,2nTn2aaaaaan1n2n2n则行列式DT称为行列式D的转置行列式。1.1.1性质1行列式与它的转置行列式相等。例题：1234132421.1.2性质2例题：34212推论：若行列式的两行（列）完全相同，则行列式为0。aaaaaa11121313331112131333DaaaDaaa11121112aaaaaa31323132D=-D,2D=0，D=01.1.3性质3行列式的某一行（列）中所有的元素都乘同一数k，等于用数k乘此行列式。例题：123124311231DD,,2,设D=这里，DD121是用=2（1*1-2*3）2D21，即D=D12第3页推论：行列式中某一行（列）所有元素的公因子可以提到行列式记号的外面。1.1.4性质4行列式中如果有两行（列）对应元素成比例，则此行列式等于0。例题：12,这里D的第二行与第一行对应元素之比为3，即两行成设D36比例，由定义得1.1.5性质5D=1*6-2*3=0例题：第i列的元素都是两数之和：aaaa()aa,i11aa12i1naa,()D2122ii2n,aaaa()a,n1n2则D等于下列两个行列式之和：aaaaaaaaa,ia11aa12i1n11aa121naa,iD21222,2122i2nnaaaaaaaa,n1n2n1n21.1.6性质6把行列式的某一列（行）的各元素乘同一数，然后加到另一列（行）对应的元素上去，行列式不变。例题：以数k乘以第j行加到第i行上，记做r+kr，有ijn2naaaaaaa1121ijai2jaan11121njkaaaaaa)ij1nc+kckakaaa)ijij()i2j2naa)n1ninjnn第4页1.1.7性质7式乘积之和。a推论：一个n