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A real, nondegenerate n×n symmetric matrix A, and its corresponding symmetric bilinear form Q(v,w)=v^(T)Aw, has signature (p,q) if there is a nondegenerate matrix C such that ...

A term used in category theory to mean a general morphism. The term derives from the Greek omicronmuomicron (omo) "alike" and muomicronrhophiomegasigmaiotasigma (morphosis), ...

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

An expression describing a form in which a quantity can be written. For example, all primes p>3 can be "represented as" 6n+/-1.

Euler's 6n+1 theorem states that every prime of the form 6n+1, (i.e., 7, 13, 19, 31, 37, 43, 61, 67, ..., which are also the primes of the form 3n+1; OEIS A002476) can be ...

A Monge patch is a patch x:U->R^3 of the form x(u,v)=(u,v,h(u,v)), (1) where U is an open set in R^2 and h:U->R is a differentiable function. The coefficients of the first ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...