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In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. [1] To say that "Property P characterizes object X" is to say that not only does X have property P, but that X is the only thing that has property P (i.e., P is a defining ...
A multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field , usually the field of complex numbers. If G is any group, then the set Ch( G ) of these morphisms forms an abelian group under pointwise multiplication.
Since the restriction of a character of G to the subgroup H is again a character of H, this definition makes it clear that θ G is a non-negative integer combination of irreducible characters of G, so is indeed a character of G. It is known as the character of G induced from θ. The defining formula of Frobenius reciprocity can be extended to ...
In linguistics, blocking is the morphological phenomenon in which a possible form for a word cannot surface because it is "blocked" by another form whose features are the most appropriate to the surface form's environment. [1] More basically, it may also be construed as the "non-occurrence of one form due to the simple existence of another." [2]
This definition is given together with a formal definition of programs (and models of computation), allowing to formally define the notion of implementation, that is when a program implements an algorithm. The notion of algorithm thus obtained avoids some known issues, and is understood as a specification of some kind.
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest positive number of copies of the ring's multiplicative identity (1) that will sum to the additive identity (0). If no such number exists, the ring is said to have characteristic zero.
In mathematics, a character group is the group of representations of an abelian group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory .
In mathematics, a characteristic class is a way of associating to each principal bundle of X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted" and whether it possesses sections.