Matlab——矩阵运算 矩阵基本变换操作

矩阵运算

+ 加 - 减 .* 乘 ./ 左除 .\ 右除 .^ 次方 .' 转置

除了加减符号，其余的运算符必须加“.”

>> a = 1:5a =1     2     3     4     5>> a-2 %减法ans =-1     0     1     2     3

>> 2.*a-1 %乘法 减法ans =1     3     5     7     9

>> b = 1:2:9b =1     3     5     7     9>> a+bans =2     5     8    11    14

>> a.*bans =1     6    15    28    45

>> a.'   %转置矩阵

ans =12345

 

 

矩阵基本变换操作

转置

>> a = [10,2,12;34,2,4;98,34,6]

a =

10 2 12
34 2 4
98 34 6

>> a.'

ans =

10 34 98
2 2 34
12 4 6

求逆

>> inv(a)ans =-0.0116    0.0372   -0.00150.0176   -0.1047    0.03450.0901   -0.0135   -0.0045

伪逆

>> pinv(a)ans =-0.0116    0.0372   -0.00150.0176   -0.1047    0.03450.0901   -0.0135   -0.0045

左右反转

>> fliplr(a)ans =12     2    104     2    346    34    98

特征值

>> [u,v]=eig(a)u =-0.2960   -0.3635    0.3600-0.2925    0.4128   -0.7886-0.9093    0.8352   -0.4985v =48.8395         0         00  -19.8451         00         0  -10.9943

上下反转

>> flipud(a)ans =98    34     634     2     410     2    12

旋转90度

>> rot90(a)ans =12     4     62     2    3410    34    98

上三角

>> triu(a)ans =10     2    120     2     40     0     6

下三角

>> tril(a)ans =10     0     034     2     098    34     6

>> [l,u] = lu(a)l =0.1020    0.1500    1.00000.3469    1.0000         01.0000         0         0u =98.0000   34.0000    6.00000   -9.7959    1.91840         0   11.1000

正交分解

>> [q,r] = qr(a)q =-0.0960   -0.1232   -0.9877-0.3263   -0.9336    0.1482-0.9404    0.3365    0.0494r =-104.2113  -32.8179   -8.09890    9.3265   -3.19410         0  -10.9638

奇异值分解

>> [u,s,v] = svd(a)u =-0.1003    0.8857    0.4532-0.3031    0.4066   -0.8618-0.9477   -0.2239    0.2277s =109.5895         0         00   12.0373         00         0    8.0778v =-0.9506    0.0619   -0.3041-0.3014   -0.4176    0.8572-0.0739    0.9065    0.4156

矩阵范数

>> norm(a)ans =109.5895>> norm(a,1)ans =142>> norm(a,inf)ans =138