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An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

A polynomial map phi_(f), with f=(f_1,...,f_n) in (K[X_1,...,X_n])^m in a field K is called invertible if there exist g_1,...,g_m in K[X_1,...,x_n] such that ...

A homotopy from one embedding of a manifold M in N to another such that at every time, it is an embedding. The notion of isotopy is category independent, so notions of ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...

A multivariate is a vector each of whose elements is a variate. The variates need not be independent, and if they are not, a correlation is said to exist between them. The ...

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

A quadratic form Q(x) is said to be positive semidefinite if it is never <0. However, unlike a positive definite quadratic form, there may exist a x!=0 such that the form is ...

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of ...