In mathematics, Gram's theorem states that an algebraic set in a finite-dimensional vector space invariant under some linear group can be defined by absolute...

case of a more general class of frequency curves. Gram's theorem, the Gram–Charlier series, and Gram points are also named after him. He died on his way...

In geometry, the Gram–Euler theorem, Gram-Sommerville, Brianchon-Gram or Gram relation (named after Jørgen Pedersen Gram, Leonhard Euler, Duncan Sommerville...

objects in differential geometry, such as instantons and monopoles. Gram's theorem Representation theory of finite groups Molien series Invariant (mathematics)...

mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors...

OEIS). A Gram block is an interval bounded by two good Gram points such that all the Gram points between them are bad. A refinement of Gram's law called...

There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information...

infinite-dimensional analog of this statement is Mercer's theorem. If M {\displaystyle M} is the Gram matrix of vectors v 1 , … , v n {\displaystyle v_{1}...

Goldbach–Euler theorem, stating that sum of 1/(k − 1), where k ranges over positive integers of the form mn for m ≥ 2 and n ≥ 2, equals 1 Gram–Euler theorem Euler's...

the major and minor axes of an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive...

preferred over the Gram–Charlier A series. Edgeworth developed a similar expansion as an improvement to the central limit theorem. The advantage of the...

In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states...

the star denotes complex conjugation. The Plancherel theorem is a special case of Parseval's theorem and states: ∑ n = 0 N − 1 | x n | 2 = 1 N ∑ k = 0 N...

Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the...

classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras. Specifically...

In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is a result used to establish bounds on the growth rates...

In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H...

finite dimensional matrix from user-input according to the representer theorem. Kernel machines are slow to compute for datasets larger than a couple...

supervision of Roger Heath-Brown. His dissertation was titled Further results on Gram's Law. Trudgian has made contributions to the field of analytic number theory...

Birthday Problem, Ramanujan Journal, 2012, [1]. Brink 2012, Theorem 2 Brink 2012, Theorem 3 Brink 2012, Table 3, Conjecture 1 "Minimal number of people...

of a directed set such that the limit exists follows using Tychonoff's theorem. The function μ A {\displaystyle \mu _{A}} is additive on disjoint compact...

In mathematics, the Farrell–Markushevich theorem, proved independently by O. J. Farrell (1899–1981) and A. I. Markushevich (1908–1979) in 1934, is a result...

integral Euclidean space Fundamental theorem of Hilbert spaces Gram–Schmidt process Hellinger–Toeplitz theorem Hilbert space Inner product space Legendre...

Discrepancy theory is based on the following classic theorems: Geometric discrepancy theory The theorem of van Aardenne-Ehrenfest Arithmetic progressions...

v2,...,vn). Proof of the Gram-Schmidt theorem is constructive, and discussed at length elsewhere. The Gram-Schmidt theorem, together with the axiom of...

positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main diagonal Diagonalizable...

independent of the location of the point. (This is an extension of Viviani's theorem.) There is a point X in the plane of the quadrilateral with the property...

square roots and to simplify relevant theorems and algorithms. Euclidean distance matrices are closely related to Gram matrices (matrices of dot products...

allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general...

by small errors from imperfect computer arithmetic. The Cayley–Hamilton theorem allows the inverse of A to be expressed in terms of det(A), traces and...