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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 ...
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.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
In applied fields the word "tight" is often used with the same meaning. [2] smooth Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion ...
Since the restriction of a character of G to the subgroup H is again a character of H, this definition makes it clear that θ G is a non-negative integer combination of irreducible characters of G, so is indeed a character of G. It is known as the character of G induced from θ. The defining formula of Frobenius reciprocity can be extended to ...
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Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.