of equations under any translation (without rotation). Discrete translational symmetry is invariant under discrete translation. Analogously, an operator...

any order are, by construction, invariant with respect to translations. Invariants ηi j with respect to both translation and scale can be constructed from...

{\cdot }\rVert } . Conversely, if a metric d on a vector space X is translation invariant: d ( x , y ) = d ( x + a , y + a ) {\displaystyle d(x,y)=d(x+a,y+a)}...

In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations...

momentum holds when the translation operators commute with the Hamiltonian, i.e. when laws of physics are translation-invariant. This is an example of...

temporal dimension. These systems may be referred to as linear translation-invariant to give the terminology the most general reach. In the case of generic...

{\displaystyle {\mathcal {B}}} is called translation-invariant if it has a base of entourages that is translation-invariant. The canonical uniformity on any commutative...

In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral...

Thus some translation invariant operations can be represented as convolution. Convolutions play an important role in the study of time-invariant systems...

some translation-invariant complete metric. Conversely, if the topology of a locally convex space X {\displaystyle X} is induced by a translation-invariant...