An Etymological Dictionary of Astronomy and Astrophysics
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Any → transformation preserving → collinearity.

→ affine; → transformation.

Empirical mathematical transformation applied to the observed magnitudes in order to convert them into a standard system, or into a different system.

→ color; → transformation.

The method of relating a measurement in one → reference frame to another moving with a constant velocity with respect to the first within the → Newtonian mechanics. The Galilean transformation between the coordinate systems (x,y,z,t) and (x',y',z',t') is expressed by the relations: x' = x - vt, y' = y, z' = z. Galilean transformations break down at high velocities and for electromagnetic phenomena and is superseded by the → Lorentz transformations.

→ Galilean; → transformation.

A change of the fields of a gauge theory that does not change the value of any measurable quantity.

→ gauge; → transformation.

A mathematical operation that transforms one function into another. Two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: df(x)/dx = (dg(x)/dx)^-1. The functions f and g are said to be related by a Legendre transformation.

→ Legendre equation; → transformation.

A set of linear equations that expresses the time and space coordinates of one → reference frame in terms of those of another one when one frame moves at a constant velocity with respect to the other. In general, the Lorentz transformation allows a change of the origin of a coordinate system, a rotation around the origin, a reversal of spatial or temporal direction, and a uniform movement along a spatial axis. If the system S'(x',y',z',t') moves at the velocity v with respect to S(x,y,z,t) in the positive direction of the x-axis, the Lorentz transformations will be: x' = γ(x - vt), y' = y, z' = z, t' = γ [t - (vx/c²)], where c is the → velocity of light and γ = [1 - (v/c)²]^-1/2. For the special case of velocities much less than c, the Lorentz transformation reduces to → Galilean transformation.

→ Lorentz; → transformation.

1) A transformation that preserves angles and changes all distances in the same ratio.
2) A transformation of the form B = X^-1AX relating two → square matrices A and B.

→ similarity; → transformation.

1) The act or process of transforming. The state of being transformed.
2) The relationship between description of a physical phenomenon in one → reference frame to another. → Galilean transformation; → Lorentz transformation.
3) Math.: The act, process, or result of transforming or mapping.

Verbal noun of → transform.

A transformation whose reciprocal is equal to its Hermitian conjugate.

→ unitary; → transformation.