1、2.4.2 行列式det 82.4.3 特征值eig 82.4.4 转置 和 . 92.4.5 变形reshape 102.4.6 翻转rot90, fliplr, flipud 112.4.7 抽取diag, tril, triu 122.5 数组运算 122.5.1 乘 12N.*MN 122.5.2 除 13N./MN 14N.M2.5.3 乘方 14N.MN 15a.M2.6 除法 152.6.1 求解线性方程组 153 多项式 163.1 系数表示法poly 163.2 求根roots 163.3 乘法conv 163.4 除法deconv 173.5 求值polyval 173.6
2、 微分polyder 181 创建矩阵1.1 直接输入 x = 1 2 3;4 5 6%实数x = 1 2 3 4 5 6 y = 3*i 3+4*j;sqrt(-1)+2 sin(3)%复数、表达式y = 0 + 3.0000i 3.0000 + 4.0000i 2.0000 + 1.0000i 0.1411 1.2 向量线性分布 x = linspace(1,10,9) % 初值,终值,元素个数1.0000 2.1250 3.2500 4.3750 5.5000 6.6250 7.7500 8.8750 10.0000 y = linspace(1,4); % 初值,终值 100个元素1.
3、2.2 冒号法 x = 1:0.8:3 %初值:间隔:终值 1.0000 1.8000 2.6000 y = 1:4.6终值 间隔为1 3 4441.3 函数创建单位矩阵 x = eye(3), y = eye(2,4) 0 0 1随机矩阵 x = rand(3), y = rand(2,4) 0.9501 0.4860 0.4565 0.2311 0.8913 0.0185 0.6068 0.7621 0.8214 0.4447 0.7919 0.7382 0.4057 0.6154 0.9218 0.1763 0.9355全0矩阵 x = zeros(3), y = zeros(2,4)全
4、1矩阵 x = ones(3), y = ones(2,4)2 矩阵运算2.1 加减N A = 1:3 ; 4:6, B = ones(2,3), C = A+B, D = A-BA =B =C = 4 6 7D = 2 52.2 乘N*a B = A*3 12 15 18M B = 1 1; 2 2; 3 3, C = A*B 14 14 32 322.3 乘方Ma6; 7:9, B = A2 7 8 30 36 42 66 81 96 102 126 150 B = 2A 1.0e+004 * 0.7962 0.9782 1.1603 1.8029 2.2154 2.6276 2.8097
5、 3.4523 4.09502.4 特殊运算2.4.1 求逆inv 4 2 9; 7 0 1, B = inv(A) 0.0256 -0.0256 0.1538 0.7564 -0.2564 0.0385 -0.1795 0.1795 -0.07692.4.2 行列式det x = det(A) 782.4.3 特征值eig C = eig(A) 8.1313 -2.0656 + 2.3078i -2.0656 - 2.3078i M = A, N = A.M = 9N = 7 0 1, B = 2*ones(3), C = A+B*i, M = C N = C. 1.0000 + 2.000
6、0i 2.0000 + 2.0000i 3.0000 + 2.0000i 4.0000 + 2.0000i 9.0000 + 2.0000i 7.0000 + 2.0000i 0 + 2.0000i 1.0000 + 2.0000i 1.0000 - 2.0000i 4.0000 - 2.0000i 7.0000 - 2.0000i 2.0000 - 2.0000i 0 - 2.0000i 3.0000 - 2.0000i 9.0000 - 2.0000i 1.0000 - 2.0000i 7.0000 + 2.0000i 0 + 2.0000i 3.0000 + 2.0000i 9.0000
7、 + 2.0000i2.4.5 变形reshape A = 1:12, B = reshape(A,3,4) , C = reshape(A, 2,6) 10 11 12 10 112.4.6 翻转rot90, fliplr, flipud B = rot90(A), C = rot90(A,-1) %90*k,k=1,2.逆时针,-1,-2.顺时针 8 B = fliplr(A), C = flipud(A)%fliplr左右翻转,flipup上下翻转2.4.7 抽取diag, tril, triu B = diag(A), C = triu(A), D = tril(A)%diag 对角线
8、,triu上三角矩阵,tril下三角矩阵2.5 数组运算2.5.1 乘 B = 1 1 1; 2 2 2, C = A.*B%同维矩阵,对应元素相乘2.5.2 除 2 2 2, C = A./B, D = A.B%同维矩阵,对应元素相除%除号,想象成杠杆撬动,上面是被除数 2.0000 3.0000 2.5000 0.5000 0.3333 0.40002.5.3 乘方 2 2 2, C = A.B 16 25 36 C = 2.A 642.6 除法2.6.1 求解线性方程组x+2y+2z=32x-y-z=6x+y-z=2 AX = B -1 -1 X = ABX = -0.5000 0.50
9、00 XA = B X = B/A 3.0000 -0.50003 多项式3.1 系数表示法poly%由根确定多项式系数,按降幂排列 x = 1 2 3, p = poly(x), poly2str(p,x) p = -6 -6ans = x3 - 6 x2 + 11 x - 63.2 求根roots%求x3 - 6 x2 + 11 x - 6 = 0的根 p = 1 -6 11 -6, x = roots(p) 2.0000 1.00003.3 乘法conv%求多项式相乘 a(x)= x2 + 2 x + 3, b(x)=4 x2 + 5 x + 6, c(x)=a(x)*b(x) a =
10、1 2 3, b = 4 6, c = conv(a,b)a =b =c = 13 28 27 poly2str(c,) 4 x4 + 13 x3 + 28 x2 + 27 x + 183.4 除法deconv%求多项式相除 a(x)= x2 + 2 , c(x)=4 x4 + 13 x3 + 28 x2 + 27 x + 18,b(x)=c(x)/a(x) c = 4 18, a = 1 0 2 b, f = deconv(c,a) %b为商,f为余式 20f = -223.5 求值polyval%求f(x)=x4 + 4 x3 + 5 x2 + 7 x - 3在x=2.6的值 f = po
11、lyval(c, 2.6) 165.00163.6 微分polyder%求多项式的一阶导数 c = 1 4 5 7 -3, fc = poly2str(c, -3fc = x4 + 4 x3 + 5 x2 + 7 x - 3 d = polyder(c), fd = poly2str(d,d =fd = 4 x3 + 12 x2 + 10 x + 7 a = 1 2 3, b = 1 3, d = polyder(a,b), e = polyder(conv(a,b)%求多项式的积的微分e = c = 1 2 3 4, a = 1 3, p, q = polyder(c,a)q =%(a/b) = p/q
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