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.

A powerful mathematical tool which is the generalization of the → Fourier series for the analysis of non-periodic functions. The Fourier transform transforms a function defined on physical space into a function defined on the space of frequencies, whose values quantify the "amount" of each periodic frequency contained in the original function. The inverse Fourier transform then reconstructs the original function from its transformed frequency components. The integral F(α) = ∫ f(u)e^-iαudu is called the Fourier transform of F(x) = (1/2π)∫ f(α)e^iαxdx, both integrals from -∞ to + ∞.

→ Fourier analysis; → transform.

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x - vt, y' = y, z' = z. Galilean transformations break down at high velocities and for electromagnetic phenomena and is superseded by the → Lorentz transformations.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.

An integral transform of a function obtained by multiplying the given function f(t) by e^-pt, where p is a new variable, and integrating with respect to t from t = 0 to t = ∞.

→ Laplace; → transform.

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) Math.: A mathematical quantity obtained from a given quantity by an algebraic, geometric, or functional transformation.
The transformation itself.
2) To change in form, appearance, or structure; to change in condition, nature, or character; convert.
Physics: To change into another form of energy.
To increase or decrease (the voltage and current characteristics of an alternating-current circuit), as by means of a transformer.
Math.: To change the form of (a figure, expression, etc.) without in general changing the value.

→ trans- + → form.

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 device that converts low voltages to higher voltages, or vice versa. A transformer consists of a primary coil and a secondary coil, both traversed by the same magnetic flux.

→ transform + → -or.

A transformation whose reciprocal is equal to its Hermitian conjugate.

→ unitary; → transformation.