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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 ...
One may interpret the character of a representation as the "twisted" dimension of a vector space. [3] Treating the character as a function of the elements of the group χ(g), its value at the identity is the dimension of the space, since χ(1) = Tr(ρ(1)) = Tr(I V) = dim(V). Accordingly, one can view the other values of the character as ...
Each character should have their distinctive voice. [14] To differentiate characters in fiction, the writer must show them doing and saying things, but a character must be defined by more than one single topic of conversation or by the character's accent. The character will have other interests or personality quirks as well. [15]
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.
In mathematics in general, a characterization theorem says that a particular object – a function, a space, etc. – is the only one that possesses properties specified in the theorem. A characterization of a probability distribution accordingly states that it is the only probability distribution that satisfies
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
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.
Literature is any collection of written work, but it is also used more narrowly for writings specifically considered to be an art form, especially novels, plays, and poems. [1] It includes both print and digital writing. [2] In recent centuries, the definition has expanded to include oral literature, much of which has been transcribed.