I want to rotate matrix as well as image and want to show that output is inavriant. Imrotate is effecting invariance so what should i do?
% Generate a random 50×30 matrix A and a 50×1 vector b
A = rand(8, 8);
b = rand(8, 1);
% A=[1 2;3 4];
% b=[1 2]’;
% Least squares solution for the original problem
x = (A’ * A) (A’ * b);
theta=90;
theta= deg2rad(theta);
% Rotation matrix for 90 degrees
R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
% Extend the rotation matrix to apply to the whole problem
R_ext = blkdiag(kron(eye(1), R), eye(0)); % Adjust size accordingly
% Rotate the matrix and vector
A_rot = R_ext * A;
b_rot= R_ext * b;
theta= rad2deg(theta);
A_rot=imrotate(A_rot,theta,’crop’);
b_rot=imrotate(b_rot,theta,’crop’);
% Display the original and rotated matrices using imagesc
% Least squares solution for the rotated problem
x_rot = (A_rot’ * A_rot) (A_rot’ * b_rot);
% Display results
fprintf(‘Original least squares solution (first 5 elements):n’);
disp(x(1:end));
fprintf(‘Rotated least squares solution (first 5 elements):n’);
disp(x_rot(1:end));
% Check invariance
invariance_check = norm(x )- norm(x_rot);
fprintf(‘Invariance check (should be close to zero): %fn’, invariance_check);I want to rotate matrix as well as image and want to show that output is inavriant. Imrotate is effecting invariance so what should i do?
% Generate a random 50×30 matrix A and a 50×1 vector b
A = rand(8, 8);
b = rand(8, 1);
% A=[1 2;3 4];
% b=[1 2]’;
% Least squares solution for the original problem
x = (A’ * A) (A’ * b);
theta=90;
theta= deg2rad(theta);
% Rotation matrix for 90 degrees
R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
% Extend the rotation matrix to apply to the whole problem
R_ext = blkdiag(kron(eye(1), R), eye(0)); % Adjust size accordingly
% Rotate the matrix and vector
A_rot = R_ext * A;
b_rot= R_ext * b;
theta= rad2deg(theta);
A_rot=imrotate(A_rot,theta,’crop’);
b_rot=imrotate(b_rot,theta,’crop’);
% Display the original and rotated matrices using imagesc
% Least squares solution for the rotated problem
x_rot = (A_rot’ * A_rot) (A_rot’ * b_rot);
% Display results
fprintf(‘Original least squares solution (first 5 elements):n’);
disp(x(1:end));
fprintf(‘Rotated least squares solution (first 5 elements):n’);
disp(x_rot(1:end));
% Check invariance
invariance_check = norm(x )- norm(x_rot);
fprintf(‘Invariance check (should be close to zero): %fn’, invariance_check); I want to rotate matrix as well as image and want to show that output is inavriant. Imrotate is effecting invariance so what should i do?
% Generate a random 50×30 matrix A and a 50×1 vector b
A = rand(8, 8);
b = rand(8, 1);
% A=[1 2;3 4];
% b=[1 2]’;
% Least squares solution for the original problem
x = (A’ * A) (A’ * b);
theta=90;
theta= deg2rad(theta);
% Rotation matrix for 90 degrees
R = [cos(theta), -sin(theta); sin(theta), cos(theta)];
% Extend the rotation matrix to apply to the whole problem
R_ext = blkdiag(kron(eye(1), R), eye(0)); % Adjust size accordingly
% Rotate the matrix and vector
A_rot = R_ext * A;
b_rot= R_ext * b;
theta= rad2deg(theta);
A_rot=imrotate(A_rot,theta,’crop’);
b_rot=imrotate(b_rot,theta,’crop’);
% Display the original and rotated matrices using imagesc
% Least squares solution for the rotated problem
x_rot = (A_rot’ * A_rot) (A_rot’ * b_rot);
% Display results
fprintf(‘Original least squares solution (first 5 elements):n’);
disp(x(1:end));
fprintf(‘Rotated least squares solution (first 5 elements):n’);
disp(x_rot(1:end));
% Check invariance
invariance_check = norm(x )- norm(x_rot);
fprintf(‘Invariance check (should be close to zero): %fn’, invariance_check); matlab MATLAB Answers — New Questions

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