矩陣運算
+ 加 - 減 .* 乘 ./ 左除 .\ 右除 .^ 次方 .' 轉置
除了加減符號，其余的運算符必須加“.”
>> a = 1:5 a = 1 2 3 4 5 >> a-2 %減法 ans = -1 0 1 2 3
>> 2.*a-1 %乘法 減法 ans = 1 3 5 7 9
>> b = 1:2:9 b = 1 3 5 7 9 >> a+b ans = 2 5 8 11 14
>> a.*b ans = 1 6 15 28 45
>> a.' %轉置矩陣 ans = 1 2 3 4 5
矩陣基本變換操作
轉置
>> 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 -0.0015 0.0176 -0.1047 0.0345 0.0901 -0.0135 -0.0045
偽逆
>> pinv(a) ans = -0.0116 0.0372 -0.0015 0.0176 -0.1047 0.0345 0.0901 -0.0135 -0.0045
左右反轉
>> fliplr(a) ans = 12 2 10 4 2 34 6 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 -0.4985 v = 48.8395 0 0 0 -19.8451 0 0 0 -10.9943
上下反轉
>> flipud(a) ans = 98 34 6 34 2 4 10 2 12
旋轉90度
>> rot90(a) ans = 12 4 6 2 2 34 10 34 98
上三角
>> triu(a) ans = 10 2 12 0 2 4 0 0 6
下三角
>> tril(a) ans = 10 0 0 34 2 0 98 34 6
>> [l,u] = lu(a) l = 0.1020 0.1500 1.0000 0.3469 1.0000 0 1.0000 0 0 u = 98.0000 34.0000 6.0000 0 -9.7959 1.9184 0 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 0.0494 r = -104.2113 -32.8179 -8.0989 0 9.3265 -3.1941 0 0 -10.9638
奇異值分解
>> [u,s,v] = svd(a) u = -0.1003 0.8857 0.4532 -0.3031 0.4066 -0.8618 -0.9477 -0.2239 0.2277 s = 109.5895 0 0 0 12.0373 0 0 0 8.0778 v = -0.9506 0.0619 -0.3041 -0.3014 -0.4176 0.8572 -0.0739 0.9065 0.4156
矩陣范數
>> norm(a) ans = 109.5895 >> norm(a,1) ans = 142 >> norm(a,inf) ans = 138