lorentz transformation in matlab

To perform Lorentz transformations in Matlab, you can use the built-in function lorentz. The function takes two input arguments: the velocity v and a 4x4 matrix A representing the coordinates of the event to be transformed. The output is also a 4x4 matrix representing the transformed coordinates.

Here's an example code snippet to transform a set of coordinates from one reference frame to another, using the Lorentz transformation:

main.m
% define a 4x4 matrix with the coordinates of the event to be transformed
A = [ct; x; y; z];

% define the velocity of the moving frame relative to the stationary frame
v = [vx; vy; vz];

% calculate the transformed coordinates using the lorentz function
B = lorentz(v,A);

% extract the transformed coordinates from the B matrix
ct_new = B(1,1);
x_new = B(2,1);
y_new = B(3,1);
z_new = B(4,1);
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In this code, ct represents the time coordinate, and x, y, and z represent the spatial coordinates. vx, vy, and vz represent the velocity of the moving reference frame in each spatial dimension. The output variables ct_new, x_new, y_new, and z_new represent the transformed coordinates in the new reference frame.

Note that the input and output matrices are in the Minkowski space, with the time coordinate as the first row and first column.