matlab实3MATLAB数学运算.doc

实验3 MATLAB数学运算 实验目的 熟悉MATLAB的矩阵运算 熟悉MATLAB的矩阵元素运算 实验内容 计算矩阵A=rand(5,5)的1阶、2阶、4阶、∞阶和Frobenius范数及其行列式、逆、秩和正交空间。 A=rand(5,5)； norm(A,1) %1-范数 norm(A,2) %或norm(A,2) 2-范数 norm4=sum(sum(abs(A)^4))^(1/4) %4-范数 norm(A,inf) %∞阶 norm(A,fro) %Frobenius范数 det(A) %求行列式 inv(A) %或A^-1 求行列式的逆 rank(A) %求行列式的秩 Q=orth(A) %求正交空间 答： A=rand(5) A = 0.9501 0.7621 0.6154 0.4057 0.0579 0.2311 0.4565 0.7919 0.9355 0.3529 0.6068 0.0185 0.9218 0.9169 0.8132 0.4860 0.8214 0.7382 0.4103 0.0099 0.8913 0.4447 0.1763 0.8936 0.1389 norm(A,1) ans = 3.5620 norm(A,2) ans = 2.8858 norm4=sum(sum(abs(A)^4))^(1/4) norm4 = 4.1769 norm(A,inf) ans = 3.2772 norm(A,fro) ans = 3.1788 det(A) ans = -0.0071 inv(A) ans = 10.9157 7.0952 -3.0741 -11.9832 -3.7273 -38.3070 -30.4335 12.7347 44.9730 15.5357 30.3119 24.1962 -10.0050 -34.2520 -13.0995 10.5097 10.0318 -4.3202 -13.2617 -3.6326 -53.4866 -43.3430 19.4471 61.7013 21.3738 rank(A) ans = 5 Q=orth(A) Q = -0.4507 0.5172 -0.0236 -0.4721 -0.5531 -0.4465 -0.2753 0.3655 0.6273 -0.4447 -0.5096 -0.6817 -0.0726 -0.4827 0.1930 -0.3984 0.3959 0.5234 0.0386 0.6396 -0.4231 0.1878 -0.7659 0.3860 0.2236 对矩阵进行LU分解、Schur分解、QR分解和奇异值分解。 答： A = 1 4 2 5 6 9 4 1 8 [L,U]=lu(A) L = 0.2000 -0.7368 1.0000 1.0000 0 0 0.8000 1.0000 0 U = 5.0000 6.0000 9.0000 0 -3.8000 0.8000 0 0 0.7895 [U,L]=schur(A) U = 0.3494 0.8929 0.2838 0.8242 -0.1489 -0.5464 0.4456 -0.4248 0.7880 L = 12.9859 -0.3899 7.2707 0 -0.4658 -3.9981 0 0 2.4799 [Q,R]=qr(A) Q = -0.1543 0.7173 0.6794 -0.7715 0.3421 -0.5364 -0.6172 -0.6070 0.5006 R = -6.4807 -5.8635