6,052 articles
Incidence matrix
An incidence matrix is a matrix recording which elements of one set are incident with elements of another, with rows for vertices and columns for edges.
Incircle
The incircle, or inscribed circle, of a triangle is the unique circle inside it tangent to all three sides, with center the incenter and radius the inradius r, satisfying K = rs.
Inclusion–exclusion principle
The inclusion–exclusion principle, or sieve principle, is a combinatorial counting formula giving the size of a union of finite sets via an alternating sum of intersections.
Income in India
Income in India is measured nationally by MoSPI through gross and net national income and per capita figures, with per capita net national income at ₹208,090 in 2025-26.
Income in the United Kingdom
Income in the United Kingdom is measured chiefly as household disposable income. Median income was £36,700 in 2024, with large gaps between regions and between rich and poor.
Incomplete block design
An incomplete block design is an experimental design in which each block receives only a subset of treatments, used when blocks cannot hold all treatments.
Incomplete gamma function
The incomplete gamma functions γ(a,z) and Γ(a,z) are the lower and upper parts of the gamma integral, used in statistics as the gamma distribution's cumulative probabilities.
Incomplete LU factorization
An incomplete LU factorization (ILU) approximates a sparse matrix as LU plus a discarded remainder R, keeping factors sparse and serving mainly as a preconditioner for Krylov methods like GMRES.
Indecomposable distribution
An indecomposable distribution, also called an indecomposable probability distribution, is one that cannot be written as a convolution of two non-degenerate distributions, like prime numbers.
Independence (probability theory)
Independence in probability theory is the property that one event's occurrence does not change the probability of another, formalized as P(A ∩ B) = P(A) · P(B).
Independence of random variables
Independence of random variables is the property that their joint distribution factors into the product of their marginals, so knowing one tells nothing about the others.
Independence polynomial
The independence polynomial, also known as the independent set polynomial or stable set polynomial, is the graph polynomial that counts a graph's independent sets by size.
Independence property (model theory)
The independence property in model theory is a combinatorial property of formulas, isolated by Shelah as a dividing line marking the boundary of NIP, or dependent, theories.
Independence test (statistics)
An independence test, or independence testing, is a statistical hypothesis test assessing whether two variables are statistically independent, using methods such as chi-squared, distance covariance, and HSIC.
Independent and identically distributed random variables
Independent and identically distributed (i.i.d. or IID) random variables are mutually independent variables that all follow the same probability distribution, modeled on repeated throws of a die.
Independent set (graph theory)
An independent set, also called a coclique or anticlique, is a set of vertices in a graph with no edges between any pair; the largest such set is the independence number.
Independent vector analysis
Independent vector analysis (IVA), introduced by Tae-Su Kim in 2007, is a blind source separation method that extends independent component analysis to several datasets at once, with applications in speech separation and fMRI.
Indescribable cardinal
An indescribable cardinal is a large cardinal whose higher-order statements about Vκ already hold in some smaller Vα, introduced by Hanf and Scott in 1961.
Indeterminate form
An indeterminate form is an expression such as 0/0 or ∞ − ∞ arising when evaluating a limit, whose limiting behaviors do not determine its value; L'Hôpital's rule resolves quotient forms.
Index (economics)
An index in economics is a statistic, usually relative to a base of 100, measuring changes in prices or quantities over time, such as the CPI.
Index coding
Index coding is a problem in network information theory on broadcasting messages efficiently to receivers that already know some of them, introduced by Birk and Kol in 1998.
Index set (computability)
In computability theory, an index set is a set of program indices that depends only on the function computed, so all programs computing the same function share membership.
Index set (recursion theory)
An index set in recursion theory is a set of program indices whose membership depends only on the set a program recognizes, not on the program text.
Indian buffet process
The Indian buffet process (IBP) is a stochastic process in Bayesian nonparametrics defining a distribution over sparse binary matrices with infinitely many columns, introduced by Griffiths and Ghahramani in 2005.
Indian mathematics
Indian mathematics is the body of mathematical work developed on the Indian subcontinent from antiquity to today, best known for giving the world the decimal place-value system with zero.
Indian numbering system
The Indian numbering system, also called the South Asian numbering system, is used in India, Pakistan, Bangladesh, Nepal, and Sri Lanka, grouping digits in twos after the first three and naming lakh (100,000) and crore (10,000,000).
Indicator function
The indicator function, also called the characteristic function of a set, maps elements of a set to 1 if they belong to a subset and 0 otherwise.
Induced representation
An induced representation is a representation of a group G built from a representation of a subgroup H, with Frobenius reciprocity making induction adjoint to restriction.
Inductive inference
Inductive inference is a recursion-theoretic theory of learning in which algorithms fed growing data samples output hypotheses converging to a correct description of an unknown object.
Inductive reasoning
Inductive reasoning, also called inductive logic or weak induction, is inference whose conclusion goes beyond its premises, so true premises support but never guarantee the conclusion.