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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 (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.

  4. 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.

  5. Characterizations of the exponential function - Wikipedia

    en.wikipedia.org/wiki/Characterizations_of_the...

    In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]

  6. Characteristic (algebra) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_(algebra)

    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.

  7. Characteristic function (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_function...

    The characteristic function is a way to describe a random variable X.The characteristic function, = ⁡ [],a function of t, determines the behavior and properties of the probability distribution of X.

  8. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.

  9. 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.