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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 (computer science), an expression whose value doesn't change during program execution Loop invariant, a property of a program loop that is true before (and after) each iteration; A data type in method overriding that is neither covariant nor contravariant; Class invariant, an invariant used to constrain objects of a class
In theoretical physics, an invariant is an observable of a physical system which remains unchanged under some transformation. Invariance, as a broader term, also applies to the no change of form of physical laws under a transformation, and is closer in scope to the mathematical definition .
In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the ...
In topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms. Alternatively, a topological property is a proper class of topological spaces which is closed under homeomorphisms.
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect ...
An invariant of two forms constructed from two invariants of each of the forms. (Elliott 1895, p.23) intermutant A special form of permutant. (Cayley 1860) invariant 1. (Adjective) Fixed by the action of a group 2. (Noun) An absolute invariant, meaning something fixed by a group action. 3.
The scalar product of a vector and a covector is invariant, because one has components that vary with the base change, and the other has components that vary oppositely, and the two effects cancel out. One thus says that covectors are dual to vectors. Thus, to summarize: