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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 ...
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.
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
Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication.
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.
Characterization or characterisation is the representation of characters (persons, creatures, or other beings) in narrative and dramatic works. The term character development is sometimes used as a synonym .
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.
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.