Lorentz Transformation Detailed Derivation

It’s worth to lay out detailed derivation of Lorentz transformation to grasp this concept deeply. So Lorentz Transformation is a linear transformation between inertial frames. Let’s assume the object is moving at constant relative velocity along the z-axis to make it simple.

Note the lambda here is basically the Jacobian matrix to transform in various inertia frames

Now let’s derive it:

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