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In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, [1] allows for multiple instances for each of its elements.The number of instances given for each element is called the multiplicity of that element in the multiset.
Multiplicity (chemistry), multiplicity in quantum chemistry is a function of angular spin momentum; Multiplicity (informatics), a type of relationship in class diagrams for Unified Modeling Language used in software engineering; Multiplicity (mathematics), the number of times an element is repeated in a multiset
If n > 0, then is a pole of order (or multiplicity) n of f. If n < 0, then is a zero of order | | of f. Simple zero and simple pole are terms used for zeroes and poles of order | | = Degree is sometimes used synonymously to order.
In mathematics, a polynomial is a ... the Greek poly, meaning "many", and the Latin nomen, or "name". ... which is called the multiplicity of a as a root of P.
Algebraic multiplicity – Multiplicity of an eigenvalue as a root of the characteristic polynomial; Geometric multiplicity – Dimension of the eigenspace associated with an eigenvalue; Gram–Schmidt process – Orthonormalization of a set of vectors; Irregular matrix; Matrix calculus – Specialized notation for multivariable calculus
The notion of the multiplicity of a module is a generalization of the degree of a projective variety. By Serre's intersection formula, it is linked to an intersection multiplicity in the intersection theory. The main focus of the theory is to detect and measure a singular point of an algebraic variety (cf. resolution of singularities).
The multiplicity of a prime factor p in n, that is the largest exponent m for which p m divides n. a 0 (n) – the sum of primes dividing n counting multiplicity, sometimes called sopfr(n), the potency of n or the integer logarithm of n (sequence A001414 in the OEIS). For example: a 0 (4) = 2 + 2 = 4 a 0 (20) = a 0 (2 2 · 5) = 2 + 2 + 5 = 9 a ...