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Cauchy matrix
A Cauchy matrix is a matrix with entries 1/(a_i − b_j) for two distinct node sets, named for Augustin-Louis Cauchy, who computed its determinant in 1841.
Cauchy problem
The Cauchy problem, also called the initial value problem, asks for the solution of a differential equation determined by data prescribed on a given initial surface.
Cauchy process
The Cauchy process is the symmetric stable Lévy process with stability index 1, whose increments follow a heavy-tailed Cauchy distribution with no finite mean or variance.
Cauchy product
The Cauchy product, also known as Cauchy multiplication, is the series formed by convolving the coefficients of two infinite series, extending polynomial multiplication; Cauchy defined it in 1821.
Cauchy sequence
A Cauchy sequence is a sequence in a metric space whose terms become arbitrarily close to each other, capturing convergence without naming a limit; it is named for Augustin-Louis Cauchy.
Cauchy transform
The Cauchy transform of a finite Borel measure on the real line is the integral of 1/(t−z), analytic in the upper half-plane; it determines the measure uniquely.
Cauchy–Davenport theorem
The Cauchy–Davenport theorem, proved by Cauchy in 1813 and rediscovered by Davenport in 1935, bounds the size of a sumset in integers modulo a prime by min(p, |A| + |B| − 1).
Cauchy–Riemann equations
The Cauchy–Riemann equations, also called the Cauchy–Riemann conditions, are a pair of partial differential equations that characterize complex differentiability, named for Augustin-Louis Cauchy and Bernhard Riemann.
Cauchy–Schwarz inequality
The Cauchy–Schwarz inequality, also called the Schwarz inequality, states that in any inner product space the inner product of two vectors never exceeds the product of their norms.
Cauchy's integral formula
Cauchy's integral formula, or Cauchy's formula, is a theorem of complex analysis stating that an analytic function inside a contour is determined by its boundary values.
Cauchy's integral theorem
Cauchy's integral theorem, also called the Cauchy–Goursat theorem, states that a holomorphic function has integral zero over any closed curve in a simply connected domain.
Causal inference
Causal inference is the process of drawing conclusions about cause and effect from data, using tools such as potential outcomes, causal graphs, and the do-operator, since causal effects cannot be measured directly.
Causal loop diagram
A causal loop diagram (CLD) is a qualitative systems map in which variables connect via positive or negative arrows, making a system's feedback loops visible.
Cavalieri's principle
Cavalieri's principle, also called the method of indivisibles, is a geometric rule stating that two solids of the same height with equal cross-sectional areas at every level have equal volumes.
Cayley graph
A Cayley graph, also called a Cayley diagram, is a graph built from a group and a generating set. Arthur Cayley introduced it in 1878 to represent abstract groups graphically.
Cayley transform
The Cayley transform is a mathematical mapping that converts unbounded self-adjoint operators on a Hilbert space into bounded ones, and also parametrizes orthogonal and unitary matrices.
Cayley tree
A Cayley tree, also called a Bethe lattice when infinite, is a branching graph in which every non-edge node connects to exactly Z neighbors with no loops.
Cayley–Dickson construction
The Cayley–Dickson construction is a method in algebra that doubles an algebra's dimension; applied to the real numbers, it yields the complex numbers, quaternions, octonions, and sedenions in turn.
Cayley–Hamilton theorem
The Cayley–Hamilton theorem, or Cayley-Hamilton, is a linear algebra result stating every square matrix satisfies its own characteristic equation; Cayley proved the 2 × 2 case in 1858.
Cayley's formula
Cayley's formula is a graph theory result, published by Arthur Cayley in 1889, stating that the number of labeled trees on n vertices is n^(n−2), most commonly proved by Prüfer's 1918 code.
Čech cohomology
Čech cohomology is a cohomology theory for topological spaces, introduced by Eduard Čech in 1932, in which cohomology groups are built from the nerves of open coverings and passed to an inverse limit.
Cell method (numerical analysis)
The cell method (CM) is a numerical method for solving field problems, developed by Enzo Tonti at the University of Trieste, which writes equations directly in discrete form.
Cellular automaton
A cellular automaton, also called a tessellation automaton, is a grid of cells, each with a finite state, updated in discrete steps by a fixed rule based on neighboring cells.
Cellular homology
Cellular homology is a technique in algebraic topology that computes the homology groups of a topological space from its CW complex structure, agreeing with singular homology.
Censored regression
Censored regression is a regression method for outcomes observed only within a range, with values beyond limits recorded at the limits; the Tobit model is its canonical form.
Censoring
Censoring is a condition in survival analysis in which only incomplete information, such as a bound rather than an exact value, is available about an event time.
Census Act 1920
The Census Act 1920 is a United Kingdom public general act providing the permanent legal framework for censuses in Great Britain, first used for the 1921 Census.
Census and Statistics Act 1905
The Census and Statistics Act 1905 is an Australian law providing the legal basis for the national census and compulsory collections by the Bureau of Statistics.
Census in the United Kingdom
The census in the United Kingdom, also known as the UK census, is an official count of the population taken every ten years since 1801, except in 1941.
Center (group theory)
The center of a group, also called the group center, is the subgroup Z(G) of elements commuting with every element, and it is normal and characteristic.