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The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

The closed graph theorem states that a linear operator between two Banach spaces X and Y is continuous iff it has a closed graph, where the "graph" {(x,f(x)):x in X} is ...

A generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation ...

A longimeter is a transparent sheet of plastic with a regular grid of lines inclined at an angle of 30 degrees to the sides of the sheet. By counting the number of squares ...