Matlab学习与实验教程-第2章MATLAB矩阵及其运算.docx

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1、第2章 MATLAB矩阵及其运算例2-1 x=l+2i; y=3-sqrt(17); z=(cos(abs(x+y)-sin(78*pi/180)/(x+abs (y) z =-0.3488 + 0.3286i例2-2 zeros(3)ans =000000000 zeros(3,2) ans000000 A=l,2,3;4,5,6;%产生一个 2x3 阶矩阵 A zeros (size (A) )%产生一个与矩阵A同样大小的零矩阵ans =000000例2-3 x=20+(50-20)*rand(5)25.897927.532538.481334.198730.549825.897927.5

2、32538.481334.198730.549844.924937.557936.491747.515828.575242.716042.611931.413437.034622.275621.618535.923943.375048.020323.897237.064734.081720.357130.113724.8655 y=0.6+sqrt(0.1)*randn(5)0.86580.31920.63170.86580.31920.63170.41020.75490.8338-0.07620.33451.02840.63921.0543-0.02011.51960.86101.03610

3、.42781.14130.26100.53750.26540.69600.53860.90390.21800.4518例2-4 M=100+magic(5)M=117124101108115123105107114116104106113120122110112119121103111118125102109例2-5 format rat%以有理形式输出 H=hilb(4)H =11/21/31/41/21/31/41/51/31/41/51/61/41/51/61/7 H=invhilb(4)H =16-120240-140-1201200-27001680240-27006480-4200

4、-1401680-42002800 format short%恢复默认输出格式 T=toeplitz(1:6)T =54321265432112342 1233 2124 3215 4326 543 p=1,0,-7,6; compan(p)ans =07-6100010例2-6 pascal(6) ans111111123456136101521141020355615153570126162156126252例2-7 A=fix(90-10+1)*rand(5)+10)A =31315451247421214229442179164383806029142456381983 P=rem(A

5、,3)=0P =0011101110010000010010000例2-8 A=4,-65,-54,0,6;56, 0, 67,-4 5,0 A =4-65-540656067 -450 k=find(A4) k =269 A(k) ans =5667 6例2-9 A=17z0,1,0,15;23,5,7,14,16;4,0,13,0,22;10,12,19,21,3;. 11,18,25,2,19; D=diag(1:5); D*A用D左乘A,对A的每行乘以一个指定常数ans =1701015461014283212039066例 2-10 A=l,2,3;l,4,9”,8,27; b=5,

6、-2,6 x=inv(A)*bx =23.0000-14.50003.6667例 2-11 p=3,-7,0,5,2, T8; A=compan(p); xl=eig(A) xl =2.1837+ O.OOOOi1.0000 +l.OOOOi1.0000l.OOOOi-0.9252+ 0.7197i-0.92520.7197i x2=roots(p) x2 =2.1837+ O.OOOOi1.0000 + l.OOOOi1.0000l.OOOOi-0.9252 +0.7197i-0.9252-0.7197i例 2-12 ch=ABcl23d4e56Fg91; subch=ch(1:5)subc

7、h =ABcl2 revch=ch(end:-1:1)revch =9gF65e4d321cBA k=find(ch=a 1&ch char(ch)%A的伴随矩阵%求A的特征值%直接求多项式p的零点茗取子字符串%将字符串倒排%找小写字母的位置国将小写字母变成相应的大写字母ans =ABC123D4E56FG9 length(k)%统计小写字母的个数ans =4例213 X=2,0,0,0,0;0,0,0,0,0;0,0,0,5,0;0,1,0,0,-1;0,0,0,0,-5; A=sparse(X)A =(1,1)2(4,2)1(3,4)5(4,5)-1(5, 5)-5例 2-14 A=2,2

8、,1;3,1,T;4,3,3;5,3,8;6,6,12; B=spconvert(A)B =(3,1)13812(2,2)(4,3)(5,3)(6,6)例215 d=-l;0;l; A=spdiags(B,d, 5, 5)A =%产生非0对角元素矩阵 国产生非。对角元素位置向量 %产生稀疏存储的系数矩阵(1,1)2(2,1)1(1,2)3(2,2)4(3,2)1(2,3)1(3,3)6(4,3)2(3,4)4(4,4)6(5,4)1(4,5)2(5,5)1f=0;3;2;1；5x=(inv(A)*f)%方程右边参数向量%求解-0.16670.11112.7222-3.61118.6111也可以采用完全存储方式来存储系数矩阵，结果如下: A=full(A)A =2300014100016400026200011 x=(inv(A)*f) * x =-0.16670.11112.7222-3.61118.6111