By Steven G. Krantz

Transparent, rigorous definitions of mathematical phrases are an important to stable medical and technical writing-and to realizing the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computing device programmers, besides lecturers, professors, and scholars, all have the necessity for understandable, operating definitions of mathematical expressions. to satisfy that desire, CRC Press proudly introduces its Dictionary of Algebra, mathematics, and Trigonometry- the second one released quantity within the CRC finished Dictionary of arithmetic. greater than 3 years in improvement, most sensible teachers and execs from prestigious associations all over the world convey you greater than 2,800 targeted definitions, written in a transparent, readable kind, whole with replacement meanings, and comparable references.From Abelian cohomology to 0 ring and from the very simple to the hugely complicated, this special lexicon comprises phrases linked to mathematics, algebra, and trigonometry, with ordinary overlap into geometry, topology, and different similar areas.Accessible but rigorous, concise yet accomplished, the Dictionary of Algebra, mathematics, and Trigonometry is your key to accuracy in writing or realizing clinical, engineering, and mathematical literature.

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See Cayley algebra. Cayley projective plane Let H be the set of all 3 × 3 Hermitian matrices M over the Cayley algebra such that M 2 = M and tr M = 1. The set H , with the structure of a projective plane, is called the Cayley projective plane. See Cayley algebra. Cayley’s Theorem Every group is isomorphic to a group of permutations. Cayley transformation The mapping between n × n matrices N and M, given by M = (I − N )(I + N )−1 , which acts as its own inverse. The Cayley transformation demonstrates a one-to-one correspondence between the real alternating matrices N and proper orthogonal matrices M with eigenvalues different from −1.

Then, the triple (V , ρ, ρ ) is said to be a coalgebra over F , provided (1V ⊗ ρ) ◦ ρ = (ρ ⊗ 1V ) ◦ ρ and (1V ⊗ ρ ) ◦ ρ = (ρ ⊗ 1V ) ◦ ρ = 1V . coalgebra homomorphism A k-linear map f : C → C , where (C, , ε) and (C , , ε ) are coalgebras over a field k, such that (f ⊗ f ) ◦ ◦ f and ε = ε ◦ f . ) for any scheme N and any natural transformation ψ : M → Hom(−, N ) there is a unique natural transformation λ : Hom(−, M) → Hom(−, N ) such that ψ = λ ◦ ϕ. coarser classification For R, S ⊂ X×X two equivalence relations on X, S is coarser than R if R ⊂ S.

See also field. commutative group See Abelian group. commutative law The requirement that a binary operation ∗, on a set X, satisfy x ∗y = y ∗x, for all x, y ∈ X. Addition and multiplication of real numbers both obey the commutative law; matrix multiplication does not. , xy = yx, for all elements x, y. ) The real numbers are a commutative ring. Rings of matrices are generally not commutative. commutator (1) An element of the form x −1 y −1 xy or xyx −1 y −1 in a group. , if and only if x and y commute.