Program for Matrix Analysis

1. Determinant

2. Singularity

3. Orthogonality

4. Inverse

5. Transpose

6. Square of matrix

4. Eigne values and eigen vectors

6. Rank of a matrix

Code: 

clc

close all

clear all

 

% A = [1 -2i; 1i -2]; % Given matrix

A = [1 2 3; 0 1 5; 5 6 0]

detA = det(A); % Determinant

fprintf('The determinant is:\n');

disp(detA);

%% Check for singularity with conditional statement

if detA == 0

fprintf('The given matrix is singular\n');

else

fprintf('The given matrix is non singular\n');

end

 

%% Check for orthogonality with conditional statement

if detA == 1 || detA == -1

fprintf('The given matrix is orthogonal\n');

else

fprintf('The given matrix is non orthogonal\n');

end

 

invA = inv(A); % Inverse

fprintf('The inverse is:\n');

disp(invA);

transA = transpose(A); % Transpose

fprintf('The transpose is:\n');

disp(transA);

squareA = A*A; % Square value of matrix

fprintf('The square of given matrix is:\n');

disp(squareA);

%% Eigne values and Eigne vectors

eigVal = eig(A); % Eigen values

fprintf('The eigen values are:\n');

disp(eigVal);

% or

[V D] = eig(A); % Eigen vectors and eigen velues

fprintf('The eigen vector and eigen values are:\n');

disp(V);

disp(D);

%% Rank

rankA = rank(A);

fprintf('The rank is:\n');

disp(rankA);

 

A =

     1     2     3

     0     1     5

     5     6     0

The determinant is:

    5.0000

The given matrix is non singular

The given matrix is non orthogonal

The inverse is:

   -6.0000    3.6000    1.4000

    5.0000   -3.0000   -1.0000

   -1.0000    0.8000    0.2000

The transpose is:

     1     0     5

     2     1     6

     3     5     0

The square of given matrix is:

    16    22    13

    25    31     5

     5    16    45

The eigen values are:

   -5.6418

   -0.1143

    7.7561

The eigen vector and eigen values are:

    0.1769   -0.7592   -0.4704

    0.5919    0.6353   -0.5250

   -0.7863   -0.1416   -0.7093

   -5.6418         0         0

         0   -0.1143         0

         0         0    7.7561

The rank is:

     3

>> 

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