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Let A be a commutative ring, let C_r be an R-module for r=0, 1, 2, ..., and define a chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0. ...

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...

Also called a chain map. Given two chain complexes C_* and D_*, a chain homomorphism is given by homomorphisms alpha_i:C_i->D_i such that alpha degreespartial_C=partial_D ...

Suppose alpha:C_*->D_* and beta:C_*->D_* are two chain homomorphisms. Then a chain homotopy is given by a sequence of maps delta_p:C_p->D_(p-1) such that partial_D ...

Chained arrow notation is a notation which generalizes the Knuth up-arrow notation and is defined as a^...^b_()_(c)=a->b->c.

A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.

A surface with tetrahedral symmetry which looks like an inflatable chair from the 1970s. It is given by the implicit equation The surface illustrated above has k=5, a=0.95, ...

A change of basis is the transformation of coordinate-based vector and operator representations in a given vector space from one vector basis representation to another.

A change of coordinates matrix, also called a transition matrix, specifies the transformation from one vector basis to another under a change of basis. For example, if ...

The partial differential equation u_(xx)+(y^2)/(1-(y^2)/(c^2))u_(yy)+yu_y=0.