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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, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. [ 1 ] Other uses of the word "character" are almost always qualified.
Chinese punctuation – Punctuation used with Chinese characters; Currency symbol – Symbol used to represent a monetary currency's name; Diacritic – Modifier mark added to a letter (accent marks etc.) Hebrew punctuation – Punctuation conventions of the Hebrew language over time; Glossary of mathematical symbols; Japanese punctuation
The Unicode Standard encodes almost all standard characters used in mathematics. [1] Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. [1] Mathematical operators and symbols are in multiple Unicode blocks. Some of these blocks are dedicated to, or ...
The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol, usually to denote a partial derivative such as / (read as "the partial derivative of z with respect to x").
An article about a mathematical object should provide an exact definition of the object, perhaps in a "Definition" section after section(s) of motivation. For example: Let S and T be topological spaces, and let f be a function from S to T. Then f is called continuous if, for every open set O in T, the preimage f −1 (O) is an open set in S.
A character χ ρ is called irreducible or simple if ρ is an irreducible representation. The degree of the character χ is the dimension of ρ; in characteristic zero this is equal to the value χ(1). A character of degree 1 is called linear. When G is finite and F has characteristic zero, the kernel of the character χ ρ is the normal subgroup:
def – define or definition. deg – degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written as.) det – determinant of a matrix or linear transformation. DFT – discrete Fourier transform.