Things named after the 19th-century French mathematician
Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy (, ; ; 21 August 178923 May 1857) was a French mathematician, engineer, and physicist who made pioneering contributions to several branches of mathematics, including mathematical analysis and continuum mechanics. He ...
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Binet–Cauchy identity
In algebra, the Binet–Cauchy identity, named after Jacques Philippe Marie Binet and Augustin-Louis Cauchy, states that
\left(\sum_^n a_i c_i\right)
\left(\sum_^n b_j d_j\right) =
\left(\sum_^n a_i d_i\right)
\left(\sum_^n b_j c_j\right)
+ \su ...
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Bolzano–Cauchy theorem
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Cauchy's argument principle
In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.
Specifically, if ' ...
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Cauchy–Binet formula In mathematics, specifically linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so tha ...
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Cauchy–Born rule
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Cauchy boundary condition
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Cauchy bounds
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Cauchy completeness
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Cauchy completion
In mathematical analysis, a metric space is called complete (or a Cauchy space) if every Cauchy sequence of points in has a limit that is also in .
Intuitively, a space is complete if there are no "points missing" from it (inside or at the boun ...
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Cauchy condensation test
In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing sequence f(n) of non-negative real numbers, the series \sum\limits_^ f(n) converges if and ...
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Cauchy-continuous function
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Cauchy's convergence test
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Cauchy (crater)
Cauchy is a small lunar impact crater on the eastern Mare Tranquillitatis. It was named after French mathematician Augustin-Louis Cauchy. It is circular and symmetric, with a small interior floor at the midpoint of the sloping inner walls. Due to ...
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Cauchy–Davenport theorem
In additive number theory and combinatorics, a restricted sumset has the form
:S=\,
where A_1,\ldots,A_n are finite nonempty subsets of a field ''F'' and P(x_1,\ldots,x_n) is a polynomial over ''F''.
If P is a constant non-zero function, for ...
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Cauchy determinant In mathematics, a Cauchy matrix, named after Augustin-Louis Cauchy, is an ''m''×''n'' matrix (mathematics), matrix with elements ''a'ij'' in the form
:
a_=;\quad x_i-y_j\neq 0,\quad 1 \le i \le m,\quad 1 \le j \le n
where x_i and y_j are elem ...
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Cauchy distribution
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Log-Cauchy distribution
In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If ''X'' is a random variable with a Cauchy distribution, then ''Y'' = exp ...
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Wrapped Cauchy distribution
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Cauchy elastic material In physics, a Cauchy-elastic material is one in which the stress at each point is determined only by the current state of deformation with respect to an arbitrary reference configuration.R. W. Ogden, 1984, ''Non-linear Elastic Deformations'', Dover, ...
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Cauchy's equation
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Cauchy–Euler equation
In mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation is a linear homogeneous ordinary differential equation with variable coefficients. It is sometimes referred to as an '' equidimensional'' equation. ...
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Cauchy's functional equation
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Cauchy filter
In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties such as completeness, uniform continuity and unif ...
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Cauchy formula for repeated integration
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Cauchy–Frobenius lemma
Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, the orbit-counting theorem, or the Lemma that is not Burnside's, is a result in group theory that is often useful in taking account of symmetry when ...
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Cauchy–Green deformation tensor
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Cauchy–Hadamard theorem
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Cauchy horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations). One side of the horizon contains closed space-like geodesics ...
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Cauchy identity
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Cauchy index In mathematical analysis, the Cauchy index is an integer associated to a real rational function over an interval. By the Routh–Hurwitz theorem, we have the following interpretation: the Cauchy index of
:''r''(''x'') = ''p''(''x'')/''q''(''x'')
...
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Cauchy inequality
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Cauchy's integral formula
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Cauchy's integral theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in t ...
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Cauchy interlacing theorem
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Cauchy–Kovalevskaya theorem
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Cauchy–Kowalevski theorem
In mathematics, the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems. A ...
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Cauchy–Lipschitz theorem
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Cauchy matrix
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Cauchy momentum equation
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Cauchy net
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Cauchy number
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Cauchy–Peano theorem
In mathematics, specifically in the study of ordinary differential equations, the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees th ...
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Cauchy point
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Cauchy principal value
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Cauchy problem
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Abstract Cauchy problem
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Cauchy process In probability theory, a Cauchy process is a type of stochastic process. There are symmetric and asymmetric forms of the Cauchy process. The unspecified term "Cauchy process" is often used to refer to the symmetric Cauchy process.
The Cauchy ...
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Cauchy product
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Cauchy's radical test
In mathematics, the root test is a criterion for the Convergent series, convergence (a convergence test) of an infinite series. It depends on the quantity
:\limsup_\sqrt
where a_n are the terms of the series, and states that the series conve ...
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Cauchy–Rassias stability A classical problem of Stanislaw Ulam in the theory of functional equations is the following: ''When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E''? In 1941, Donald H. Hye ...
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Cauchy ratio test
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Cauchy–Riemann equations
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Cauchy–Riemann manifold
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Cauchy's Residue Theorem
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Cauchy–Schlömilch transformation
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Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is considered one of the most important and widely used inequalities in mathematics.
The inequality for sums was published by . The corresponding inequality fo ...
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Cauchy sequence
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Uniformly Cauchy sequence In mathematics, a sequence of functions \ from a set ''S'' to a metric space ''M'' is said to be uniformly Cauchy if:
* For all \varepsilon > 0, there exists N>0 such that for all x\in S: d(f_(x), f_(x)) N.
Another way of saying this is that d_u ...
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Cauchy space
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Cauchy surface
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Cauchy's mean value theorem
In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc (geometry), arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant line, secant ...
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Cauchy stress tensor
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Cauchy's theorem (geometry)
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that
convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the fac ...
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Cauchy's theorem (group theory)
In mathematics, specifically group theory, Cauchy's theorem states that if is a finite group and is a prime number dividing the order of (the number of elements in ), then contains an element of order . That is, there is in such that is t ...
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Cauchy's two-line notation
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Euler–Cauchy stress principle
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Maclaurin–Cauchy test
In mathematics, the integral test for convergence is a convergence tests, method used to test infinite series (mathematics), series of Monotonic function, monotonous terms for convergent series, convergence. It was developed by Colin Maclaurin a ...
{{DEFAULTSORT:List Of Topics Named After Augustin-Louis Cauchy
Cauchy