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Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., ...

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...

If M^n is a finite simplicial complex of dimension n>=5 that has the homotopy type of the sphere S^n and is locally piecewise linearly homeomorphic to the Euclidean space ...

An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension. The most common use of an ...

A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.