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The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

Lucas's theorem states that if n>=3 be a squarefree integer and Phi_n(z) a cyclotomic polynomial, then Phi_n(z)=U_n^2(z)-(-1)^((n-1)/2)nzV_n^2(z), (1) where U_n(z) and V_n(z) ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

The extended mean-value theorem (Anton 1984, pp. 543-544), also known as the Cauchy mean-value theorem (Anton 1984, pp. 543) and Cauchy's mean-value formula (Apostol 1967, p. ...

The fourth group isomorphism theorem, also called the lattice group isomorphism theorem, lets G be a group and let N⊴G, where N⊴G indicates that N is a normal subgroup of G. ...