Search results
Results from the WOW.Com Content Network
The phrases "invariant under" and "invariant to" a transformation are both used. More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class. [3] Invariants are used in diverse areas of mathematics such as geometry, topology, algebra and discrete mathematics. Some important ...
Invariant (mathematics), a property of a mathematical object that is not changed by a specific operation or transformation Rotational invariance , the property of function whose value does not change when arbitrary rotations are applied to its argument
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set.
The single, scalar value of mass is independent to changes in basis vectors and consequently is called invariant. The magnitude of a vector (such as distance ) is another example of an invariant, because it remains fixed even if geometrical vector components vary.
In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the characteristic polynomial [1]
Classically, the term "invariant theory" refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. This was a major field of study in the latter part of the nineteenth century.
In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by T. More generally, an invariant subspace for a collection of linear mappings is a subspace preserved by each mapping individually.
A subgroup of a group is called a normal subgroup of if it is invariant under conjugation; that is, the conjugation of an element of by an element of is always in . [3] The usual notation for this relation is N G {\displaystyle N\triangleleft G} .