Matlab exercises -- routine operation of matrix

matlab Series articles ： Catalog

One 、 subject

Let's set the matrix
$$A=\left(\begin{array}{ccc}4& -2& 2\\ -3& 0& 5\\ 1& 5& 3\end{array}\right),B=\left(\begin{array}{ccc}1& 3& 4\\ -2& 0& 3\\ 2& -1& 1\end{array}\right)$$

• (1) Extract matrix $A$ First 、 Three elements , matrix $B$ First 、 The three column ; Commutative matrix $A$ First 、 Two lines , matrix $B$ First 、 Two columns ;
• (2) Delete matrix $A$ The second line of , Delete matrix $B$ The second column of ;
• (3) Calculation $|A|$,$|B|$,$A^{-1}$,$B^{-1}$,$A$、$B$ Eigenvalues and eigenvectors of ,$A$、$B$ The transpose matrix of , The matrix $A$ Upside down 、 matrix $B$ Turn left and right , Calculation of matrix $A$ The maximum and average values of each row of 、 The minimum value of each column , The output matrix $B$ The row and column positions of the largest and smallest elements 、 Merge matrix $A$ and $B$;
• (4) Calculation $A+B$,$A-B$,$AB$,$BA$,$A^2$,$A^{\ast }B$,$A/B$.

Two 、 answer

① Create two matrices ：

>> A = [4 -2 2;-3 0 5;1 5 3]	% Create a matrix A

A =

     4    -2     2
    -3     0     5
     1     5     3

>> B = [1 3 4;-2 0 3;2 -1 1]	% Create a matrix B

B =

     1     3     4
    -2     0     3
     2    -1     1

Topic 1

1. Extract matrix A One 、 Three elements

>> A([1 3],:)

ans =

     4    -2     2
     1     5     3

2. Extract matrix B One 、 The three column

>> B(:,[1 3])

ans =

     1     4
    -2     3
     2     1

3. Commutative matrix A First 、 Two lines

>> A([1 2],:) = A([2 1],:)

A =

    -3     0     5
     4    -2     2
     1     5     3

4. Commutative matrix B First 、 Two columns

>> B(:,[1 2]) = B(:,[2 1])

B =

     3     1     4
     0    -2     3
    -1     2     1

Topic two

1. Delete matrix A The second line of

>> A([2],:) = []

A =

    -3     0     5
     1     5     3

2. Delete matrix B The second column of

>> B(:,[2]) = []

B =

     3     4
     0     3
    -1     1

Question three

1. Calculation $|A|$,$|B|$

>> det(A)

ans =

  -158

>> det(B)

ans =

    35

2. Calculation $A^{-1}$、$B^{-1}$

>> inv(A)

ans =

    0.1582   -0.1013    0.0633
   -0.0886   -0.0633    0.1646
    0.0949    0.1392    0.0380

>> inv(B)

ans =

    0.0857   -0.2000    0.2571
    0.2286   -0.2000   -0.3143
    0.0571    0.2000    0.1714

3. Calculation $A$、$B$ Eigenvalues and eigenvectors of

>> [x1,y1] = eig(A)

x1 =

    0.3055    0.8054    0.2410
    0.7795    0.0974    0.5208
   -0.5469    0.5847    0.8189


y1 =

   -4.6842         0         0
         0    5.2102         0
         0         0    6.4740



>> [x2,y2] = eig(B)

x2 =

   Column  1  to  2

   0.8210 + 0.0000i  -0.0719 + 0.5666i
   0.0181 + 0.0000i  -0.7330 + 0.0000i
   0.5706 + 0.0000i   0.1776 - 0.3240i

   Column  3

  -0.0719 - 0.5666i
  -0.7330 + 0.0000i
   0.1776 + 0.3240i


y2 =

   Column  1  to  2

   3.8461 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i  -0.9230 + 2.8720i
   0.0000 + 0.0000i   0.0000 + 0.0000i

   Column  3

   0.0000 + 0.0000i
   0.0000 + 0.0000i
  -0.9230 - 2.8720i

4. seek $A$、$B$ The transpose matrix of

>> A.'

ans =

     4    -3     1
    -2     0     5
     2     5     3

>> B.'

ans =

     1    -2     2
     3     0    -1
     4     3     1

5. The matrix $A$ Upside down 、 matrix $B$ Turn left and right

>> flipud(A)

ans =

     1     5     3
    -3     0     5
     4    -2     2

>> fliplr(B)

ans =

     4     3     1
     3     0    -2
     1    -1     2

6. Calculation of matrix $A$ The maximum and average values of each row of 、 The minimum value of each column

① Calculation $A$ The maximum value per line of

>> max(A,[],2)

ans =

     4
     5
     5

② Calculation $A$ Mean value per line of

>> mean(A,2)

ans =

    1.3333
    0.6667
    3.0000

③ Calculation $A$ The minimum value of each column of

>> min(A,[],1)

ans =

    -3    -2     2

7. The output matrix $B$ The row and column positions of the largest and smallest elements

① The output matrix $B$ The row and column position of the largest element

>> [x,y] = find(B==max(max(B)))

x =

     1


y =

     3
     
>> for i = 1:length(x)
fprintf('[%d,%d]\n',x(i),y(i))
end
[1,3]

① The output matrix $B$ The row and column position of the smallest element

>> [x,y] = find(B==min(min(B)))

x =

     2


y =

     1

>> for i = 1:length(x)
fprintf('[%d,%d]\n',x(i),y(i))
end
[2,1]

8. Merge matrix $A$ and $B$

>> [A,B]

ans =

     4    -2     2     1     3     4
    -3     0     5    -2     0     3
     1     5     3     2    -1     1

Question 4

1. Calculation $A+B$

>> A+B

ans =

     5     1     6
    -5     0     8
     3     4     4

2. Calculation $A-B$

>> A-B

ans =

     3    -5    -2
    -1     0     2
    -1     6     2

3. Calculation $AB$

>> A*B

ans =

    12    10    12
     7   -14    -7
    -3     0    22

4. Calculation $BA$

>> B*A

ans =

    -1    18    29
    -5    19     5
    12     1     2

5. Calculation $A^2$

>> A*A

ans =

    24     2     4
    -7    31     9
    -8    13    36

6. Calculation $A^{\ast }B$

>> inv(A)*det(A)*B

ans =

  -77.0000  -65.0000  -62.0000
  -58.0000   68.0000   60.0000
   17.0000  -39.0000 -132.0000

7. Calculation $A/B$

>> A/B

ans =

         0         0    2.0000
    0.0286    1.6000    0.0857
    1.4000   -0.6000   -0.8000