目錄

• MATLAB Cookbook
  • Linear Algebra
    • 共軛轉置 '
    • 轉置.'
    • 【如何】得到向量中的元素個數？
    • dot product 點乘
    • outer product 外積
    • cross product 叉乘
    • extract submatrix 擷取矩陣
    • row interchanging 行交換

MATLAB Cookbook

• 該筆記整理自Using MATLAB in Linear Algebra, Edward Neuman Department of Mathematics Southern Illinois University at Carbondale

Linear Algebra

共軛轉置 '

>> a = [1 2 3];
>> b = [1;2;3];
>> (a+i*b')'

ans =

   1.0000 - 1.0000i
   2.0000 - 2.0000i
   3.0000 - 3.0000i

轉置.'

>> a = [1 2 3];
>> b = [1;2;3];
>> (a+i*b').'

ans =

   1.0000 + 1.0000i
   2.0000 + 2.0000i
   3.0000 + 3.0000i

【如何】得到向量中的元素個數？

length(a)

>> a = [1 2 3];
>> length(a)

ans =

     3
 

使用.來表示分量components之間的運算

It is used for the componentwise application of the operator that follows the dot operator

dot product 點乘

>> a = [1 2 3];
>> b = [1;2;3];
>> a*b

ans =

    14

outer product 外積

>> a = [1 2 3];
>> b = [1;2;3];
>> b*a

ans =

     1     2     3
     2     4     6
     3     6     9
 

cross product 叉乘

>> a = [1;2;3];
>> b = [-2 1 2];
>> cross(a,b)

ans =

     1    -8     5

>> a = [1 2 3];
>> b = [-2 1 2];
>> cross(a,b)

ans =

     1    -8     5
% 無論是列向量還是行向量，結果都一樣

extract submatrix 擷取矩陣

% To extract a submatrix
>> A = [1 2 3;4 5 6;7 8 10];
>> B = A([1 3],[1 2]) % 選取第1,3行，1,2列，得到由該行列所選中的元素組成的矩陣

B =

     1     2
     7     8

row interchanging 行交換

% 使用 : 來選中所有列，重新選取特定行組成新的矩陣。
>> A = [1 2 3;4 5 6;7 8 10];
>> C = A([3 2 1],:)

C =

     7     8    10
     4     5     6
     1     2     3

• The colon operator : stands for all columns or all rows.