as coordinate transformations at an event between local inertial reference frames

The Lorentz transformations may therefore be thought of as coordinate transformations at an event between local inertial reference frames.

a one- parameter family of linear transformations from a coordinate frame in space time to another frame that moves at a constant velocity

Features heavy duty weatherproof physics the Lorentz transformations are a one- parameter family of linear transformations from a coordinate frame in space time to another frame that moves at a constant velocity, the parameter within the former.

a mathematical transformation of space-time coordinates of a physical event

Lorentz transformation is known that Lorentz transformation is a mathematical transformation of space-time coordinates of a physical event.

a six-parameter family of linear transformations

Lorentz transformations are a six-parameter family of linear transformations that relate the values of the coordinates of an event in one inertial reference system to the coordinates of the same event in another inertial system that moves at a constant velocity relative to the former.

to transformations between inertial frames, usually in the context of special relativity

The term 'Lorentz transformations' only refers to transformations between inertial frames, usually in the context of special relativity.

Poincaré transformations and linear/homogeneous Poincaré transformations

Poincaré transformations and linear/homogeneous Poincaré transformations are called Lorentz transformations.

to hyperbolic rotations

The distance metric is not Euclidean, a hyperbolic geometry is hyperbolic, and Lorentz transformations correspond to hyperbolic rotations.

examples of linear transformations

Lorentz transformations are examples of linear transformations; general isometries of Minkowski spacetime are affine transformations.

in accordance with Albert Einstein's special relativity

The Lorentz transformation is in accordance with Albert Einstein's special relativity, but was derived first.

coordinates of events in one reference frame

Lorentz transformations relate coordinates of events in one reference frame to those of another frame.

a rotation in four-dimensional space about the origin by introducing as a fourth imaginary coordinate

Max Abraham noticed that the Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing as a fourth imaginary coordinate, and Max Abraham used an early form of four-vectors.

squeeze mappings, the linear transformations that turn a square into a rectangles of the same area

In mathematical terms, Lorentz transformations are squeeze mappings, the linear transformations that turn a square into a rectangles of the same area.

Those isometries that leave the origin fixed

Those isometries that leave the origin fixed are called Lorentz transformations and give rise to the symmetry known as Lorentz covariance.

the basis of Einstein's special theory of relativity

Lorentz transformations, which Heike Kamerlingh Onnes introduced in 1904, form the basis of Einstein's special theory of relativity.

linear transformations on the tangent spaces, induced by a coordinate transformation

Either way, the Lorentz transformations $\mathrm{SO}(1,3)$ are linear transformations on the tangent spaces, induced by a coordinate transformation.

at the heart of special relativity

Lorentz transformations are at the heart of special relativity.

the deciding factor in the transition from one such system

In contrast to classical mechanics; the Lorentz transformation is the deciding factor in the transition from one such system to another.