An Abelian group is a group with a binary additive operation (+), satisfying the group axioms: closure associativity existence of additive identity existence of additive opposite commutativity of addition
|BanachSpace<B,F extends Field<F> & Comparable<F>>||
A Banach space, B, is a complete normed vector space such that every Cauchy sequence (with respect to the metric d(x, y) = |x - y|) in B has a limit in B.
As an algebraic structure, every field is a ring, but not every ring is a field.
|HilbertSpace<H,F extends Field<F> & Comparable<F>>||
A Hilbert space is an inner product space, an abstract vector space in which distances and angles can be measured.
A monoid is a group with a binary operation (×), satisfying the group axioms: closure associativity existence of multiplicative identity
A ring is a set R equipped with two binary operations called addition and multiplication:
|VectorSpace<V,F extends Field<F>>||
A vector space is a set V together with two binary operations that combine two entities to yield a third, called vector addition and scalar multiplication.
This is the exception thrown when the inverse of a field element does not exist.
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