6,052 articles
Intuitionistic logic
Intuitionistic logic, also called constructivist logic, is a logic without the law of excluded middle, abstracted by L. E. J. Brouwer's intuitionistic mathematics and formalized by Arend Heyting in 1930.
Invariant measure
An invariant measure, also called a stationary measure, is a measure left unchanged by a transformation, flow, or Markov kernel, central to ergodic theory and Markov chains.
Invariant subspace
An invariant subspace is a subspace of a vector space that a linear operator maps into itself, the concept underlying eigenvectors, the Jordan canonical form, and a famous open problem.
Invariant theory
Invariant theory is the branch of mathematics that studies polynomial functions left unchanged by a group action, classically begun in Arthur Cayley's 1845 paper and central to Hilbert's finiteness theorem.
Invasive weed optimization
Invasive weed optimization, also known as the invasive weed optimization algorithm, is a population-based metaheuristic for numerical optimization introduced by Mehrabian and Lucas in 2006.
Inverse distance weighting
Inverse distance weighting, also known as Shepard's method, is a spatial interpolation method proposed by Donald Shepard in 1968 that weights nearby measured values by inverse distance.
Inverse eigenvalue problem
The inverse eigenvalue problem asks whether a matrix with prescribed eigenvalues exists within a given structural class, such as symmetric or nonnegative matrices, and how to construct it.
Inverse function
An inverse function is a function that reverses another function, sending each output back to its input. It exists only when the function is bijective.
Inverse function theorem
The inverse function theorem of calculus states that a continuously differentiable map between open sets is locally invertible, with a differentiable inverse, wherever its derivative is invertible.
Inverse Galois problem
The inverse Galois problem asks whether every finite group occurs as the Galois group of a finite Galois extension of the rational numbers; it remains open in general.
Inverse Gaussian distribution
The inverse Gaussian distribution, also called the Wald distribution, is a continuous probability distribution on positive numbers, arising as the first passage time of Brownian motion.
Inverse hyperbolic functions
The inverse hyperbolic functions, also known as the area hyperbolic functions, are the six inverses of the hyperbolic functions, written arcsinh, arccosh, arctanh, and the reciprocals.
Inverse iteration
Inverse iteration is an eigenvalue algorithm that finds the eigenvector whose eigenvalue lies nearest a chosen shift, working by the power method applied to the inverse shifted matrix.
Inverse limit
The inverse limit, also called the projective limit, is a mathematical construction that assembles objects connected by backward-pointing maps into a single object of compatible choices, used across algebra, topology, and number theory.
Inverse probability weighting
Inverse probability weighting (IPW) is a statistical technique that weights each observed unit by the reciprocal of its probability of being observed, correcting selection bias.
Inverse scattering
Inverse scattering is a mathematical method that reconstructs an object's shape or a medium's refractive index and scattering potential from measurements of scattered waves, a nonlinear and ill-posed problem.
Inverse scattering transform
The inverse scattering transform, also called the nonlinear Fourier transform, solves integrable nonlinear PDEs like the KdV equation by converting them into linear scattering problems.
Inverse semigroup
An inverse semigroup is a semigroup in which every element has a unique inverse, the algebraic structure capturing partial symmetries, defined independently by Vagner and Preston in the 1950s.
Inverse transform sampling
Inverse transform sampling, also called inversion, generates random samples from a probability distribution by applying the inverse of its cumulative distribution function to a uniform random number.
Inverse trigonometric functions
The inverse trigonometric functions, also known as cyclometric or arc functions, are six functions that invert the sine, cosine, and tangent to return the angle for a given value.
Inverse-gamma distribution
The inverse-gamma distribution, or inverted gamma distribution, is a continuous probability distribution obtained as the reciprocal of a gamma-distributed variable, used mainly as a conjugate prior for a normal variance.
Inversion theorem (probability theory)
An inversion theorem in probability theory recovers a probability distribution, its density, or mass function from a transform, most famously via the Lévy inversion theorem for characteristic functions.
Invertible matrix
An invertible matrix, also called a non-singular matrix, is a square matrix with an inverse that multiplies it to give the identity; such an inverse exists exactly when the determinant is nonzero.
Involute
An involute of a plane curve is the curve traced by the end of a taut string unwound from it, described by Christiaan Huygens in 1673.
Involution (mathematics)
An involution in mathematics is a function that is its own inverse, so applying it twice gives back the original; examples include negation, reciprocals, and complex conjugation.
IPOPT
IPOPT, short for Interior Point OPTimizer, is an open-source software library for large-scale nonlinear optimization of continuous systems, developed under COIN-OR since 2002 by Andreas Wächter and Carl Laird.
Iris flower data set
The iris flower data set, also known as Fisher's Iris data set, is a collection of 150 flower measurements in three iris species, published by R. A. Fisher in 1936.
Irrational number
An irrational number is a real number that cannot be written as a ratio of two integers; its decimal expansion neither terminates nor repeats, as with √2 and π.
Irrational rotation algebra
The irrational rotation algebra, also called the noncommutative torus, is a universal C-algebra generated by two unitaries with uv = e^(2πiθ)vu; for irrational θ it is simple with a unique trace.
Irreducible element
An irreducible element, also called an atom, is a nonzero, non-unit element of an integral domain that cannot be written as a product of two non-unit elements; it generalizes prime numbers to abstract rings.