《用数学软件Mathematica做线性代数》由会员分享，可在线阅读，更多相关《用数学软件Mathematica做线性代数（34页珍藏版）》请在金锄头文库上搜索。
1、用数学软件Mathematica做线性代数作者：徐小湛四川大学数学学院目 录前言第一章 行列式 行列式 DetA 克拉默法则第二章 矩阵及其运算 矩阵的线性运算 矩阵的乘法 A.B 矩阵的转置 TransposeA 逆矩阵 InverseA 矩阵方程第三章 矩阵的初等变换与线性方程组矩阵的行最简形 RowReduceA 矩阵的秩 MatrixRankA齐次线性方程组 基础解系 NullSpaceA非齐次线性方程组 求特解 LinearSolveA,b用Solve求线性方程组的解第四章 向量组的线性相关性向量的线性表示 极大无关组第五章 相似矩阵及二次型正交矩阵 矩阵的特征值 Eigenvalu
2、esA 矩阵的特征向量 EigenvectorsA 矩阵的对角化矩阵的正交化 OrthogonalizeP 二次型的标准化参考文献前 言Mathematica是著名的数学软件，具有强大的的数学运算能力和绘图功能。本文档用Mathematica来进行线性代数中的各种运算。 本文档中所有的例子都是用Mathematica 7编程和计算的，有的命令在版本较低的Mathematica可能无法执行。另外，有的运算结果拷贝到Word时，格式有些变化，但是在Mathematica中的输出格式没有问题。如有对本文档中的内容任何问题，请发邮件与作者讨论。邮箱： xuxz2010-9-4返回目录第一章 行列式行列
3、式 DetA例 计算三阶行列式（同济5版，3页）输入：A=1,2,-4,-2,2,1,-3,4,-2；DetA输出：-14例 计算四阶行列式（同济5版，12页）输入：A=3,1,-1,2,-5,1,3,-4,2,0,1,-1,1,-5,3,-3;DetA输出：40例 求解方程（同济5版，3页）输入：A:=1,1,1,2,3,x,4,9,x2SolveDetA0,x输出：x2,x3例 计算行列式（同济5版，13页）输入：A=a,b,c,d,a,a+b,a+b+c,a+b+c+d,a,2a+b,3a+2b+c,4a+3b+2c+d,a,3a+b,6a+3b+c,10a+6b+3c+d;A/Matr
4、ixForm （给出A的矩阵形式）DetA输出：(NoBreak a, b, c, d, a, a+b, a+b+c, a+b+c+d, a, 2 a+b, 3 a+2 b+c, 4 a+3 b+2 c+d, a, 3 a+b, 6 a+3 b+c, 10 a+6 b+3 c+d NoBreak) （给出A的矩阵形式）a4 例 计算行列式（同济5版，15页）输入：A=a,0,0,0,0,b,0,a,0,0,b,0,0,0,a,b,0,0,0,0,c,d,0,0,0,c,0,0,d,0,c,0,0,0,0,d;A/MatrixFormDetAFactor%（将结果因式分解）输出-b3 c3+3
5、a b2 c2 d-3 a2 b c d2+a3 d3-(b c-a d)3例 计算范德蒙行列式（同济5版，18页）输入：Van=Tablexjk,k,0,4,j,1,5%/MatrixFormDetVan输出：1,1,1,1,1,x1,x2,x3,x4,x5,x12,x22,x32,x42,x52,x13,x23,x33,x43,x53,x14,x24,x34,x44,x54(NoBreak 1, 1, 1, 1, 1, x1, x2, x3, x4, x5, x12, x22, x32, x42, x52, x13, x23, x33, x43, x53, x14, x24, x34, x
6、44, x54 NoBreak)x14 x23 x32 x4-x13 x24 x32 x4-x14 x22 x33 x4+x12 x24 x33 x4+x13 x22 x34 x4-x12 x23 x34 x4-x14 x23 x3 x42+x13 x24 x3 x42+x14 x2 x33 x42-x1 x24 x33 x42-x13 x2 x34 x42+x1 x23 x34 x42+x14 x22 x3 x43-x12 x24 x3 x43-x14 x2 x32 x43+x1 x24 x32 x43+x12 x2 x34 x43-x1 x22 x34 x43-x13 x22 x3 x44
7、+x12 x23 x3 x44+x13 x2 x32 x44-x1 x23 x32 x44-x12 x2 x33 x44+x1 x22 x33 x44-x14 x23 x32 x5+x13 x24 x32 x5+x14 x22 x33 x5-x12 x24 x33 x5-x13 x22 x34 x5+x12 x23 x34 x5+x14 x23 x42 x5-x13 x24 x42 x5-x14 x33 x42 x5+x24 x33 x42 x5+x13 x34 x42 x5-x23 x34 x42 x5-x14 x22 x43 x5+x12 x24 x43 x5+x14 x32 x43 x5
8、-x24 x32 x43 x5-x12 x34 x43 x5+x22 x34 x43 x5+x13 x22 x44 x5-x12 x23 x44 x5-x13 x32 x44 x5+x23 x32 x44 x5+x12 x33 x44 x5-x22 x33 x44 x5+x14 x23 x3 x52-x13 x24 x3 x52-x14 x2 x33 x52+x1 x24 x33 x52+x13 x2 x34 x52-x1 x23 x34 x52-x14 x23 x4 x52+x13 x24 x4 x52+x14 x33 x4 x52-x24 x33 x4 x52-x13 x34 x4 x52
9、+x23 x34 x4 x52+x14 x2 x43 x52-x1 x24 x43 x52-x14 x3 x43 x52+x24 x3 x43 x52+x1 x34 x43 x52-x2 x34 x43 x52-x13 x2 x44 x52+x1 x23 x44 x52+x13 x3 x44 x52-x23 x3 x44 x52-x1 x33 x44 x52+x2 x33 x44 x52-x14 x22 x3 x53+x12 x24 x3 x53+x14 x2 x32 x53-x1 x24 x32 x53-x12 x2 x34 x53+x1 x22 x34 x53+x14 x22 x4 x53
10、-x12 x24 x4 x53-x14 x32 x4 x53+x24 x32 x4 x53+x12 x34 x4 x53-x22 x34 x4 x53-x14 x2 x42 x53+x1 x24 x42 x53+x14 x3 x42 x53-x24 x3 x42 x53-x1 x34 x42 x53+x2 x34 x42 x53+x12 x2 x44 x53-x1 x22 x44 x53-x12 x3 x44 x53+x22 x3 x44 x53+x1 x32 x44 x53-x2 x32 x44 x53+x13 x22 x3 x54-x12 x23 x3 x54-x13 x2 x32 x54
11、+x1 x23 x32 x54+x12 x2 x33 x54-x1 x22 x33 x54-x13 x22 x4 x54+x12 x23 x4 x54+x13 x32 x4 x54-x23 x32 x4 x54-x12 x33 x4 x54+x22 x33 x4 x54+x13 x2 x42 x54-x1 x23 x42 x54-x13 x3 x42 x54+x23 x3 x42 x54+x1 x33 x42 x54-x2 x33 x42 x54-x12 x2 x43 x54+x1 x22 x43 x54+x12 x3 x43 x54-x22 x3 x43 x54-x1 x32 x43 x54+x2 x32 x43 x54结果太复杂，应化简。输入：DetVan/Simplify （化简以上结果）或 FactorDetVan （因式分解以上结果）
