Sinkhorn's theorem
Sinkhorn's theorem states that every square matrix with positive entries can be written in a certain standard form.
Gerbaldi's theorem
In linear algebra and projective geometry, Gerbaldi's theorem, proved by Gerbaldi, states that one can find six pairwise apolar linearly independent nondegenerate ternary quadratic forms. These are pe
Spectral theorem
In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matri
Rouché–Capelli theorem
In linear algebra, the Rouché–Capelli theorem determines the number of solutions for a system of linear equations, given the rank of its augmented matrix and coefficient matrix. The theorem is various
Schur's theorem
In discrete mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur. In functional analysis, Schu
MacMahon's master theorem
In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis (1916)
Chebotarev theorem on roots of unity
The Chebotarev theorem on roots of unity was originally a conjecture made by Ostrowski in the context of lacunary series. Chebotarev was the first to prove it, in the 1930s. This proof involves tools
Cramer's rule
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It express
Sylvester's law of inertia
Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of basis. Namely, if A is the
Witt's theorem
In mathematics, Witt's theorem, named after Ernst Witt, is a basic result in the algebraic theory of quadratic forms: any isometry between two subspaces of a nonsingular quadratic space over a field k
Perron–Frobenius theorem
In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron and Georg Frobenius, asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the co
Weinstein–Aronszajn identity
In mathematics, the Weinstein–Aronszajn identity states that if and are matrices of size m × n and n × m respectively (either or both of which may be infinite) then,provided (and hence, also ) is of t
Goddard–Thorn theorem
In mathematics, and in particular in the mathematical background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem describing properties of a functor that qua
Cayley–Hamilton theorem
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or co
Principal axis theorem
In the mathematical fields of geometry and linear algebra, a principal axis is a certain line in a Euclidean space associated with an ellipsoid or hyperboloid, generalizing the major and minor axes of
Fundamental theorem of linear algebra
In mathematics, the fundamental theorem of linear algebra is a collection of statements regarding vector spaces and linear algebra, popularized by Gilbert Strang. The naming of these results is not un
Schur–Horn theorem
In mathematics, particularly linear algebra, the Schur–Horn theorem, named after Issai Schur and Alfred Horn, characterizes the diagonal of a Hermitian matrix with given eigenvalues. It has inspired i
Dimension theorem for vector spaces
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is
Rank–nullity theorem
The rank–nullity theorem is a theorem in linear algebra, which asserts that the dimension of the domain of a linear map is the sum of its rank (the dimension of its image) and its nullity (the dimensi
Specht's theorem
In mathematics, Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940. Two m
Hawkins–Simon condition
The Hawkins–Simon condition refers to a result in mathematical economics, attributed to David Hawkins and Herbert A. Simon, that guarantees the existence of a non-negative output vector that solves th
Sylvester's determinant identity
In matrix theory, Sylvester's determinant identity is an identity useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this identity without proof