What Is the Linear Form of the Lorentz Transformation Equation?

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SUMMARY

The linear form of the Lorentz transformation equations for a Lorentz boost in the x-direction is defined as follows: x' = g(x - vt) and t' = g(t - vx), where g = sqrt(1 - v²) in units where the speed of light c = 1. This transformation allows for the calculation of coordinates in different inertial frames moving relative to each other at a constant velocity. To achieve the full Lorentz transformations, one can incorporate additional directions and rotations, leading to inhomogeneous Lorentz transformations, also known as Poincaré transformations.

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can anybody give me just equation of the transformation in a linear form ? without any complications just the equation of Lt. 10x
 
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Lorentz-Boost in x-direction:
x'=g(x-vt)
t'=g(t-vx)
g=sqrt(1-v²)
in units where c=1.

You can add different directions and rotations to obtain the full Lorentz-Transformations, and translations to obtain inhomogenous LT, sometimes called Poincaré Transformations.
 

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