Sentence examples for a group of transformations from inspiring English sources

Do they need to know what constitutes a "group of transformations" or a "complex number"?

In a gauge theory there is a group of transformations of the field variables (gauge transformations) that leaves the basic physics of the quantum field unchanged.

In each case they are able to do so because the relevant theory presents them with a group of transformations that converts one observer's measurements into another's and leaves the appropriate basic quantities invariant.

To generalize condition (2), we need a group of transformations acting on M, with respect to which the invariance condition is to be formulated.

Invariant theory is concerned with expressions that remain constant (invariant) under a group of transformations.

A group of symmetry transformations is a mathematical object which consists of the set of transformations, including the identity transformation and the inverse of each transformation, and the operation of composing them, where the result of two composed transformations is itself in the original set.

For any problem, we have a group of admissible transformations, those that change the problem into an equivalent form.

The main idea behind all these special forms is the invariance of a configuration of elements under a group of automorphic transformations.

Its group of automorphisms is generated (as a group of projective transformations) by ( a (x_0, x_1, y) : = (x_0, epsilon x_1, y)) where (epsilon ) is a primitive sixth root of 1, and by ( b (x_0, x_1, y) : = (x_1, x_0, i y)). a has order 6, b has order 4, the square (b^2) is the hyperelliptic involution (h (x_0, x_1, y) : = (x_0, x_1, -y)).

Cauer discovered that all solutions for the realisation of a given impedance expression could be obtained from one given solution by a group of affine transformations.

In her 1915 paper, Noether found a solution to the finite basis problem for a finite group of transformations G acting on a finite-dimensional vector space over a field of characteristic zero.