In mathematics, the Poincaré separation theorem, also known as the Cauchy interlacing theorem, gives some upper and lower bounds of eigenvalues of a real...

Euler–Poincaré characteristic Neumann–Poincaré operator Reflecting Function Here is a list of theorems proved by Poincaré: Poincaré's recurrence theorem: certain...

Poincaré: Euler–Poincaré characteristic Hilbert–Poincaré series Poincaré–Bendixson theorem Poincaré–Birkhoff theorem Poincaré–Birkhoff–Witt theorem,...

inequality Weyl's inequality in matrix theory Cauchy interlacing theorem Poincaré separation theorem Bonse's inequality Large sieve inequality Pólya–Vinogradov...

Academic Press. p. 441. ISBN 0-12-088735-5. Saul Stahl (1993). "Theorem 8.3". The Poincaré half-plane: a gateway to modern geometry. Jones & Bartlett Learning...

Kolmogorov width. Condition number Cauchy interlacing theorem or Poincaré separation theorem Schur–Horn theorem Singular value decomposition R. A. Horn and C...

theorem (Fourier analysis) Plancherel theorem for spherical functions (representation theory) Poincaré–Bendixson theorem (dynamical systems) Poincaré–Birkhoff–Witt...

conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture), Fermat's...

angle of parallelism that depends on their separation. This study became widely accessible through the Poincaré disc model where motions are given by Möbius...

Max Dehn. Poincaré pioneered the study of three-dimensional manifolds and raised a fundamental question about them, today known as the Poincaré conjecture...

Hewitt & Ross 1970, Theorem 27.40. Mackey 1976, section 2.4. Banaszczyk 1983. Hatcher 2001, Theorem 4.66. Hatcher 2001, Theorem 3C.4. Edwards 1995, p...

The metrization theorems provide necessary and sufficient conditions for a topology to come from a metric. The Baire category theorem says: If X is a...

Poincaré, Alfred Bucherer (1903) believed in the validity of the relativity principle within the domain of electrodynamics, but contrary to Poincaré,...

dimensionality. In contrast, for continuous dynamical systems, the Poincaré–Bendixson theorem shows that a strange attractor can only arise in three or more...

for a minimal surface Liouville's equation Ricci flow, used to prove the Poincaré conjecture Tzitzeica equation Rabinovich–Fabrikant equations General Legendre...

Euclidean distance) is the Poincaré group (as opposed to the Galilean group). In his second relativity paper in 1905, Henri Poincaré showed how, by taking...

be regarded as special cases of various forms of the Poincaré inequality, with the optimal Poincaré constant identified explicitly. The middle version is...

intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier...

l'équation de Poincaré, Einstein et Planck: Henri Poincare et la physique". E = mc2 l'équation de Poincaré, Einstein et Planck: Henri Poincare et la physique...

publisher (link) Murzi, Mauro. "Henri Poincaré". Internet Encyclopedia of Philosophy. Includes a discussion of Poincaré's critique of the Peano's axioms. Podnieks...

representation of the Poincaré group under which the field operators transform covariantly. Wightman's paper with D. Hall reported to a theorem that stated that...

vol. 9, no. 30, pp. 27–80 (Poincaré quoted from Kline 1982) Dunham, William (1991). Journey through Genius: The Great Theorems of Mathematics. Penguin....

notable applications, they are the fundamental tool in the proof of the Poincaré conjecture from geometric topology. Partly due to this variety of sources...

varieties. In French. Henri Poincaré, Analysis Situs, Journal de l'École Polytechnique ser 2, 1 (1895) pages 1–123. Henri Poincaré, Complément à l'Analysis...

category theorem Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's...

space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs. In a phase space, every degree of freedom or...

Pythagorean theorem about 1500 years before Pythagoras and the Indian Sulba Sutras around 800 BC contained the first statements of the theorem; the Egyptians...

"lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures...

of infinite cardinal numbers and the continuum hypothesis. 1895 – Henri Poincaré publishes paper "Analysis Situs" which started modern topology. 1896 –...

Serre duality can be viewed as an analog of Poincaré duality. It also leads to the Riemann–Roch theorem for projective curves, i.e., projective varieties...