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  2. Characterization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Characterization_(mathematics)

    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 ...

  3. Character theory - Wikipedia

    en.wikipedia.org/wiki/Character_theory

    In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form.

  4. Character (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Character_(mathematics)

    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.

  5. Information theory - Wikipedia

    en.wikipedia.org/wiki/Information_theory

    In the case of communication of information over a noisy channel, this abstract concept was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication, in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver ...

  6. A Mathematical Theory of Communication - Wikipedia

    en.wikipedia.org/wiki/A_Mathematical_Theory_of...

    Shannon's article laid out the basic elements of communication: An information source that produces a message; A transmitter that operates on the message to create a signal which can be sent through a channel; A channel, which is the medium over which the signal, carrying the information that composes the message, is sent

  7. Communication - Wikipedia

    en.wikipedia.org/wiki/Communication

    In a different sense, the term communication refers to the message that is being communicated or to the field of inquiry studying communicational phenomena. [5] The precise characterization of communication is disputed. Many scholars have raised doubts that any single definition can capture the term accurately.

  8. Character group - Wikipedia

    en.wikipedia.org/wiki/Character_group

    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 .

  9. Faithful representation - Wikipedia

    en.wikipedia.org/wiki/Faithful_representation

    In mathematics, especially in an area of abstract algebra known as representation theory, a faithful representation ρ of a group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings ρ(g).

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