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multiplicity
(redirected from Multiplicity of a restricted root)

   Also found in: Legal, Wikipedia 0.01 sec.
multiplicity
Physics the number of levels into which the energy of an atom, molecule, or nucleus splits as a result of coupling between orbital angular momentum and spin angular momentum

multiplicity [‚məl·tə′plis·əd·ē]
(mathematics)
A root of a polynomial ƒ(x) has multiplicitynif (x - a)nis a factor of ƒ(x) andnis the largest possible integer for which this is true.
The geometric multiplicity of an eigenvalue λ of a linear transformationTis the dimension of the null space of the transformationT - λI, whereIdenotes the identity transformation.
The algebraic multiplicity of an eigenvalue λ of a linear transformationTon a finite-dimensional vector space is the multiplicity of λ as a root of the characteristic polynomial ofT.
(physics)
In a system having Russell-Saunders coupling, the quantity 2S+1, whereSis the total spin quantum number.


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