In mathematics, the subspace theorem says that points of small height in projective space lie in a finite number of hyperplanes. It is a result obtained...

analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace of some vector space...

the collection of all the subspaces is then represented by a projection-valued measure. One formulation of the spectral theorem expresses the operator A...

lattice points in some convex bodies. In the geometry of numbers, the subspace theorem was obtained by Wolfgang M. Schmidt in 1972. It states that if n is...

Lomonosov's invariant subspace theorem is a mathematical theorem from functional analysis concerning the existence of invariant subspaces of a linear operator...

In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by...

and in particular all pushouts. Theorem. Let the topological space X be covered by the interiors of two subspaces X1, X2 and let A be a set which meets...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

is a closed linear operator defined on a dense linear subspace of X. The Hille–Yosida theorem provides a necessary and sufficient condition for a closed...

excision theorem is a theorem about relative homology and one of the Eilenberg–Steenrod axioms. Given a topological space X {\displaystyle X} and subspaces A...

Milman–Pettis theorem (Banach space) Moore–Aronszajn theorem (Hilbert space) Orlicz–Pettis theorem (functional analysis) Quotient of subspace theorem (functional...

theorem see the Bing metrization theorem. Separable metrizable spaces can also be characterized as those spaces which are homeomorphic to a subspace of...

functional analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz...

c{\sqrt[{4}]{n}}} . Quotient of subspace theorem, or Milman's M*-estimate, concerns the geometry of proportional-dimensional subspaces and quotients, showing that...

Pietro Corvaja gave a new proof by using a new method based on the subspace theorem. Siegel's result was ineffective for g ≥ 2 {\displaystyle g\geq 2}...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

In mathematics, the quotient of subspace theorem is an important property of finite-dimensional normed spaces, discovered by Vitali Milman. Let (X, ||·||)...

Diophantine equations. There is a higher-dimensional version, Schmidt's subspace theorem, of the basic result. There are also numerous extensions, for example...

a subspace, there exists a projection from the ambient space onto c 0 {\displaystyle c_{0}} whose norm is at most 2 {\displaystyle 2} . The theorem is...

background of string theory, the Goddard–Thorn theorem (also called the no-ghost theorem) is a theorem describing properties of a functor that quantizes...

are sequentially compact in the subspace topology – are precisely the closed and bounded subsets. This form of the theorem makes especially clear the analogy...

(1): 174–179. doi:10.4064/sm-3-1-174-179. Willard 2004, Theorem 25.5. "Are proper linear subspaces of Banach spaces always meager?". https://www.ams...

orthogonal projection P onto a subspace of dimension m such that PAP* = B. The Cauchy interlacing theorem states: Theorem. If the eigenvalues of A are α1...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

2 has a non-trivial invariant subspace. The spectral theorem shows that all normal operators admit invariant subspaces. Aronszajn & Smith (1954) proved...

say that the Wigner–Eckart theorem is a theorem that tells how vector operators behave in a subspace. Within a given subspace, a component of a vector operator...

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

Quillen–Suslin theorem implies that every algebraic vector bundle over an affine space is trivial. Affine hull – Smallest affine subspace that contains...

k < i. This means that si is in the linear subspace of Qm spanned by the set of the cj's. Folkman's theorem, the statement that there exist arbitrarily...

usually denoted by ρ(V). The Hodge index theorem says that the subspace spanned by H in D has a complementary subspace on which the intersection pairing is...