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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 theory is a branch of abstract algebra dealing with actions of groups ... "Über die vollen Invariantensysteme (On Full Invariant Systems)", Math. Annalen ...
In mathematics, particularly in topology and knot theory, Arnold invariants are invariants introduced by Vladimir Arnold in 1994 [1] for studying the topology and geometry of plane curves. The three main invariants— J + {\displaystyle J^{+}} , J − {\displaystyle J^{-}} , and S t {\displaystyle St} —provide ways to classify and understand ...
In mathematics, an invariant measure is a measure that is preserved by some function. The function may be a geometric transformation . For examples, circular angle is invariant under rotation, hyperbolic angle is invariant under squeeze mapping , and a difference of slopes is invariant under shear mapping .
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.
In mathematics, in the fields of multilinear algebra and representation theory, the principal invariants of the second rank tensor are the coefficients of the ...
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 mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context.