l???????? MATLAB 常用數學函數

這些數學函數一般都可以作為矩陣函數。

a=1:1:10;

b=0:10:90;

sin(a)

ans =

? Columns 1 through 7

??? 0.8415??? 0.9093??? 0.1411?? -0.7568?? -0.9589??-0.2794??? 0.6570

? Columns 8 through 10

0.9894???0.4121?? -0.5440

exp(b)

ans =

? 1.0e+039 *

? Columns 1 through 7

??? 0.0000??? 0.0000??? 0.0000??? 0.0000??? 0.0000??? 0.0000??? 0.0000

? Columns 8 through 10

??? 0.0000??? 0.0001??? 1.2204

sign(a)

ans =

???? 1???? 1???? 1???? 1???? 1???? 1???? 1???? 1???? 1???? 1

mean(b)

ans =

??? 45

l????????求矩陣的長度的函數

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

?size(a)

ans =

3?????????????????3

?length(a)

ans =

3

好好的看一下兩者之間的區別。

l????????矩陣的幾種基本變換操作

1.?????? 通過在矩陣變量后加’的方法來表示轉置運算

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

?a'

ans =

??? 10??? 34??? 98

???? 2???? 2??? 34

12???? 4???? 6

2.?????? 矩陣求逆

?inv(a)

ans =

?? -0.0116 ???0.0372?? -0.0015

??? 0.0176?? -0.1047??? 0.0345

??? 0.0901?? -0.0135?? -0.0045

3.?????? 矩陣求偽逆

?pinv(a)

ans =

?? -0.0116??? 0.0372?? -0.0015

??? 0.0176?? -0.1047??? 0.0345

??? 0.0901?? -0.0135?? -0.0045

4.?????? 左右反轉

?fliplr(a)

ans =

??? 12???? 2??? 10

???? 4???? 2??? 34

???? 6??? 34??? 98

5.?????? 矩陣的特征值

?[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

6.?????? 上下反轉

?flipud(a)

ans =

??? 98??? 34???? 6

??? 34???? 2???? 4

10???? 2??? 12

7.?????? 旋轉90度

?rot90(a)

ans =

??? 12?? ??4???? 6

???? 2???? 2??? 34

10??? 34??? 98

8.?????? 取出上三角和下三角

?triu(a)

ans =

??? 10??? ?2??? 12

???? 0???? 2???? 4

???? 0???? 0???? 6

?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

9.?????? 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

10．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

11．求矩陣的范數

?norm(a)

ans =

? 109.5895

?norm(a,1)

ans =

?? 142

?norm(a,inf)

ans =

?? 138

總結

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