boost matrix in three dimensions coordinates in matlab

To boost a matrix in three dimensions, you can use the boost function in MATLAB. The idea is to first define a four-vector (x,y,z,t) that represents the four-dimensional space-time of the matrix, and then apply a boost to this four-vector to transform it to a new frame of reference.

Here's an example code block that demonstrates how to boost a matrix using the boost function in MATLAB:

main.m
% Define the matrix coordinates in 3D
x = [1 2 3; 4 5 6; 7 8 9];
y = [1 1 1; 2 2 2; 3 3 3];
z = [1 1 1; 1 1 1; 1 1 1];

% Define the velocity vector for the boost
v = [0.5 0.5 0.5];

% Define the space-time four-vector for the matrix
t = 0;
fourvec = [x(:)'; y(:)'; z(:)'; t*ones(1,numel(x))];
fourvec = fourvec';

% Apply the boost to the four-vector
boosted_fourvec = boost(v,fourvec);

% Reshape the boosted four-vector back into a 3D matrix
boosted_x = reshape(boosted_fourvec(:,1),size(x));
boosted_y = reshape(boosted_fourvec(:,2),size(y));
boosted_z = reshape(boosted_fourvec(:,3),size(z));

% Plot the boosted matrix
figure; hold on;
scatter3(boosted_x(:),boosted_y(:),boosted_z(:),'filled','r');
scatter3(x(:),y(:),z(:),'filled','b');
legend('Boosted Matrix','Original Matrix');
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In this code block, we first define the matrix coordinates x, y, and z in 3D. We then define a velocity vector v that represents the boost we want to apply to the matrix. We create a space-time four-vector for the matrix by concatenating the x, y, and z coordinates with a time-coordinate t. We then apply the boost function to this four-vector with the velocity vector v. Finally, we reshape the boosted four-vector back into a 3D matrix, and plot the original and boosted matrices using the scatter3 function.