generate random matrix with selected determinant in matlab

To generate a random matrix of a specific determinant in MATLAB, use the det function along with the randn function. randn generates a matrix with normally distributed random numbers, and the determinant can be adjusted by multiplying the matrix with a scalar value. Here's an example code snippet that generates a random 3x3 matrix with a determinant of 10:

main.m
% Set the matrix size
n = 3;

% Set the target determinant
det_value = 10;

% Initialize the determinant
det_matrix = 0;

% Generate a random matrix with the desired determinant
while det_matrix ~= det_value
    % Generate a matrix with normally distributed random numbers
    A = randn(n);

    % Multiply the matrix with a scalar to adjust the determinant
    multiplier = det_value / det(A);
    A = A * multiplier;

    % Calculate the determinant of the matrix
    det_matrix = det(A);
end

% Display the matrix and its determinant
disp('Random matrix with determinant 10:');
disp(A);
disp(['Determinant: ' num2str(det_matrix)]);
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Note that the generated matrix may not always be exactly the target determinant due to the random number generation process, so the code uses a loop to generate a matrix until the determinant matches the target value.

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