Single Sentence definition of Lorentz Transform

Question

Dear fellow physics lovers,
After having spent some significant time to understand the Lorentz Transformations the following is the most simple and complete single sentence definition of it that I have been able to think of.
A Lorentz Transform (also known as a Lorentz Boost) are a Set of Linear Equations that Transform the Percieved Position $vec{r}$ of an Object O and Percieved Ellapsed Time
from the Point of View of a Static Observer A to the Point of View of a Non-Static Observer B which is moving at a relative Constant Velocity $vec{v}$ with respect to Observer A after a certain Ellapsed Time t.
Please let me know whether the above qualifies as a correct single sentence definition of Lorentz Transform.
Please correct me if I am wrong. I will appreciate if someone can provide a simpler / more appropriate single sentence definition that does not involve usage of primed and unprimed coordinates
and/or variables and also does not use the words spacetime and frame
The goal is to update the definition Lorentz Transformation in Wikipedia with this single sentence. I think it will be useful to many people who have just begun to learn about
Special Relativity/Lorentz Transform from the Internet.

Kasi Reddy Sreeman Reddy · Accepted Answer

You are almost correct. But

A Lorentz Transform (also known as a Lorentz Boost) ...

this statement of yours is not correct. A Lorentz transformation is not exactly the same as the Lorentz boost. Even if two different coordinates systems are such that one is just a rotation of the other and each is at rest with respect to the other, their transformation is still considered as a Lorentz transformation. A Lorentz boost is a rotation-free Lorentz transformation.

... View of a Static Observer A to the Point of View of a Non-Static Observer B which is moving at a relative Constant Velocity $bar{v}$ with respect to Observer A after a certain Elapsed Time t.

Even this statement is not completely correct. You have to replace observer with the coordinate system. A coordinate system is a group of imaginary clocks that are synchronized. If you consider a point observer then the observer is a single clock. The observer does not measure the time we get from the transformations, he actually measures the time after considering the time taken for light to reach him from the position where the event happened. Also, you are specifying static observer and nonstatic observer, if you are saying this with respect to one of the observers it is correct, but if you are assuming one of them is at absolute rest then that is wrong as it violates the first postulate of Special Relativity.
Also, don't update the definitions on Wikipedia, they are technically more correct.
Edit: (Some points from Comments)
Every 3d rotation can be expressed as a Lorentz transformation. Also, center inversion and mirror inversions are also Lorentz transformations.
If the velocity of A with respect to B is v then the difference in velocities of A and B with respect to C won't have a magnitude v in general. This is only possible in some cases like where A and B are moving in the same direction with respect to C. In general, it is not true. The reason is a consequence of the fact that consecutive nonparallel Loretz boosts are not Lorentz boosts. It actually is a product of a pure rotation and a pure Lorentz boost.
A good reference where these are properly discussed is https://www.google.co.in/books/edition/Special_Relativity/U3fADwAAQBAJ?hl=en&gbpv=1&printsec=frontcover

RogerJBarlow · Answer

'Elapsed' time is unhelpful. It implies two times, a start and a finish.
It is wrong to talk about 'static' and 'non-static' observers. Both observers have to be on an equal footing.
Any $x,y,z,t$ refers to an event. Not an object (except by coincidence). This area of SR is all about events and their co-ordinates, and any definition of the Lorentz Transformtion should be framed in this language.

Omar Nagib · Answer

Let me give you a correct definition of the Lorentz Transformation (LT):
It is a linear transformation between the spacetime coordinates of two inertial reference frames in relative motion that satisfy 1) the principle of relativity and 2) The constancy of the speed of light in all inertial reference frames.
Your definition fails for the following:

It is generic/ not unique to the LT. Your definition could as well apply to the Galilean transformation. This is because your definition does not specify the two above conditions that must be satisfied by the LT (especially condition 2).

Your definition refers to the transformation of single points in space (i.e., positions) and elapsed times (i.e., time intervals). Actually, LT (and even Galilean transformation) transforms spacetime events between two inertial coordinates. A spacetime event is something that happens at single point in space and time (i.e., instant). Meanwhile, elapsed time refers to an interval which is the difference between two instants*.

Your definition fails to specify that the transformation must be linear.

In the last sentence you say

with respect to Observer A after a certain Elapsed Time t.

Even if we were to disregard the previous point about elapsed times, this fails to specify elapsed time with respect to which observer (A? B? other?). Elapsed times are in fact relative in LT.
*Of course, LT allows you to transform time and space intervals (i.e., the difference between two positions and the difference between their corresponding instants) between two inertial frames. But in your definition, you say it transforms position (i.e., point in space, an event) after elapsed time t (the difference between two points in time, a time interval). This is inconsistent. You should either stick to events or intervals.

Single Sentence definition of Lorentz Transform

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