定义矩阵，向量:

(%i1)A:matrix([1,2,3],[-2,8,3],[1,4,9]);

(%o1)[1 2 3]

         [-2 8 3]

         [1 4 9]

(%i2)v:[2,3,5];

(%o2)[2 3 5]

把行向量变为列向量：

(%i3)v:transpose([2,3,5]);

(%o3)[2]

         [3]

         [5]

(%i4)v:matrix([2],[3],[5]);

(%o4)[2]

         [3]

         [5]

矩陣的表示和截取:

定义符号矩阵：

(%i1)A:matrix([a[1,1],a[1,2]],[a[2,1],a[2,2]]);

(%o1)[a1,1   a1,2]

         [a2,1   a2,2]

C为常数：

(%i2)C*A;

(%o2)[a1,1C   a1,2C]

         [a2,1C   a2,2C]

定义常数矩阵：

(%i3)B:matrix([1,2,3],[-2,8,3],[1,4,9]);

(%o3)[1 2 3]

         [-2 8 3]

         [1 4 9]

提取矩阵B中1行元素：

(%i4)row(B,1);

(%o4)[1 2 3]

提取矩阵B中2列元素：

(%i5)col(B,2);

(%o5)[2]

         [8]

         [4]

提取矩阵B中2行3列元素：

(%i6)B[2,3];

(%o6)3

矩阵的四则运算：
(%i1)A:matrix([9,4,2],[2,9,3],[0,1,4]);
(%o1)[9 4 2]
(%i2)B:matrix([2,8,1],[8,3,4],[6,4,0]);
(%o2)[2 8 1]
(%i3)5*A;
(%o3)[45 20 10]
(%i4)A+B;
(%o4)[11 12 3]
(%i5)A-B;
(%o5)[7 -4 1]
(%i6)A.B; 矩阵的乘
(%o6)[62 92 25]
(%i7)A*B; 对应元素相乘
(%o7)[18 32 2 ]

矩阵相关函数：
(%i1)A:matrix([1,2,3],[-2,8,3],[1,4,9]);
(%o1) [ 1 2 3]
(%i2)transpose(A); 矩阵转置
(%o2)[1 -2 1]
(%i3)determinant(A); 矩阵行列式
(%o3)54
(%i4)adjoint(A); 伴随矩阵
(%o4)[60 -6 -18]
(%i5)invert(A); 反矩阵
(%o5)[10/9 -1/9 -1/3 ]
(%i6)echelon(A); 梯形矩阵
(%o6)[1 2 3 ]
(%i7)diagmatrix(4,5);4*4阶对角矩阵，对角元素为5
(%o7)[5 0 0 0]
(%i8)m:[2*x+y+z=7,x-4*y+3*z=2,3*x+2*y+2*z=13]$
(%i9)augcoefmatrix(m,[x,y,z]);线性方程组系数矩阵
(%o9)[2 1 1 -7 ]
(%i10)B:matrix([4,0,1],[2,3,2],[1,0,4]);
(%o10)[4 0 1]
(%i11)load("nchrpl")$加载相关软件包，调用函数mattrace()
(%i12)mattrace(B);求矩阵B的对角元素之和
(%o12)11
(%i13)eigenvalues(B);矩阵B的特征值为[5,3]
(%o13)[[5,3],[1,2]]
(%i14)eigenvectors(B);
矩阵B的特征向量,5对应[1,2,1],3对应[1,0,-1],[0,1,0]
(%o14)[[[5,3],[1,2]],[1,2,1],[1,0,-1],[0,1,0]]
(%i15)determinant(B-digamatrix(length(B),x));
求矩阵B特征多项式
(%o15)x+(3-x)(4-x)2-3
(%i16)expand(%o15); 展开
(%o16)-x3+11x2-39x+45

(%i17)eq1:x+2*y+3*z=6$
(%i18)eq2:2*x-3*y+2*z=14$
(%i19)eq3:3*x+y-z=-2$
(%i20)solve([eq1,eq2,eq3],[x,y,z]);解线性方程组
(%o20)[[x=1,y=-2,z=3]]

矩阵定义：
(%i1) n: 3$
(%i2) m: entermatrix (n, n)$

Is the matrix 1. Diagonal 2. Symmetric 3. Antisymmetric 4. General
Answer 1, 2, 3 or 4 : 1
选择1对角矩阵;2符号矩阵;3反符号矩阵;4一般矩阵
Row 1 Column 1: (a+b)^n$
Row 2 Column 2: (a+b)^(n+1)$
Row 3 Column 3: (a+b)^(n+2)$

Matrix entered.
(%i3) m;
(%o3)[ (b + a)^3 0 0 ]
(%i4)F[i,j]:=1/(i+j-1)$
(%i5)genmatrix(F,3,3);由函数产生矩阵
(%o5)[1 1/2 1/3]