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For example, density (mass divided by volume, in units of kg/m 3) is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size".
Calculus. In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [1] [2] [3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules .
Quotient group. A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers ...
Quotient ring. In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring [1] or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. [2] [3] It is a specific example of a quotient, as viewed from the general setting ...
The cokernel of a linear operator T : V → W is defined to be the quotient space W/im(T). Quotient of a Banach space by a subspace. If X is a Banach space and M is a closed subspace of X, then the quotient X/M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section.
Ideal quotient. In abstract algebra, if I and J are ideals of a commutative ring R, their ideal quotient ( I : J) is the set. Then ( I : J) is itself an ideal in R. The ideal quotient is viewed as a quotient because if and only if . The ideal quotient is useful for calculating primary decompositions. It also arises in the description of the set ...
Quotient category. In mathematics, a quotient category is a category obtained from another category by identifying sets of morphisms. Formally, it is a quotient object in the category of (locally small) categories, analogous to a quotient group or quotient space, but in the categorical setting.
Quotient graph. In graph theory, a quotient graph Q of a graph G is a graph whose vertices are blocks of a partition of the vertices of G and where block B is adjacent to block C if some vertex in B is adjacent to some vertex in C with respect to the edge set of G. [1] In other words, if G has edge set E and vertex set V and R is the ...
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