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A residual is generally a quantity left over at the end of a process. It may refer to:


Business

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Residual (entertainment industry) Residuals are financial compensations that are paid to the actors, film or television directors, and others involved in making TV shows and movies in cases of reruns, syndication, DVD release, or online streaming release. Residuals are calculated ...
, in business, one of an ongoing stream of royalties for rerunning or reusing motion pictures, television shows or commercials *
Profit (accounting) Profit, in accounting, is an income distributed to the ownership , owner in a Profit (economics) , profitable market production process (business). Profit is a measure of profitability which is the owner's major interest in the income-formati ...
, residuals that shareholders, partners or other owners are entitled to, after debtors are covered **Residual in the bankruptcy of
insolvent In accounting, insolvency is the state of being unable to pay the debts, by a person or company (debtor), at maturity; those in a state of insolvency are said to be ''insolvent''. There are two forms: cash-flow insolvency and balance-sheet inso ...
businesses, moneys that are left after all assets are sold and all creditors paid, to be divided among ''residual claimants'' * Residual (or balloon) in finance, a lump sum owed to the financier at the end of a loan's term; for example
Balloon payment mortgage A balloon payment mortgage is a mortgage which does not fully amortize over the term of the note, thus leaving a balance due at maturity.Wiedemer, John P, ''Real Estate Finance, 8th Edition'', p 109-110 The final payment is called a ''balloon pa ...


Mathematics, statistics and econometrics

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Residual (statistics) In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The err ...
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Studentized residual In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student's ''t''-statistic, with the estimate of error varying between points. This is ...
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Residual time In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between any given time t and the next epoch of the renewal process under consideration. In the context ...
, in the theory of renewal processes *
Residual (numerical analysis) Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find ''x'' such that : f(x)=b. Given an approximation ''x''0 of ''x'', the residual is : b - f(x_0) that is, "what is left of the right hand side" after ...
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Minimal residual method In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with ...
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Generalized minimal residual method In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with ...
* Residual set, the complement of a
meager set In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is small or negligible in a precise sense detailed below. A set that is not meagre is called ...
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Residual property (mathematics) In the mathematical field of group theory, a group is residually ''X'' (where ''X'' is some property of groups) if it "can be recovered from groups with property ''X''". Formally, a group ''G'' is residually ''X'' if for every non-trivial element ' ...
, a concept in group theory *
Residually finite group {{unsourced, date=September 2022 In the mathematical field of group theory, a group ''G'' is residually finite or finitely approximable if for every element ''g'' that is not the identity in ''G'' there is a homomorphism ''h'' from ''G'' to a finit ...
, a specific residual property * The residual function attached to a
residuated mapping In mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. It refines the concept of a monotone function. If ''A'', ''B'' are posets, a function ''f'': ''A'' → ''B'' is defined to be monotone if it is o ...
* Residual in a
residuated lattice In abstract algebra, a residuated lattice is an algebraic structure that is simultaneously a lattice ''x'' ≤ ''y'' and a monoid ''x''•''y'' which admits operations ''x''\''z'' and ''z''/''y'', loosely analogous to division or implication, when ' ...
, loosely analogous to division *
Residue (complex analysis) In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for an ...
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Solow residual The Solow residual is a number describing empirical productivity growth in an economy from year to year and decade to decade. Robert Solow, the Nobel Memorial Prize in Economic Sciences-winning economist, defined rising productivity as rising output ...
, in economics


Geomorphology

A ''residual'' is the remnant of a formerly extensive mass of rock or land surface *
Inselberg An inselberg or monadnock () is an isolated rock hill, knob, ridge, or small mountain that rises abruptly from a gently sloping or virtually level surrounding plain. In Southern Africa a similar formation of granite is known as a koppie, a ...
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Mesa A mesa is an isolated, flat-topped elevation, ridge or hill, which is bounded from all sides by steep escarpments and stands distinctly above a surrounding plain. Mesas characteristically consist of flat-lying soft sedimentary rocks capped by ...
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Monadnock An inselberg or monadnock () is an isolated rock hill, knob, ridge, or small mountain that rises abruptly from a gently sloping or virtually level surrounding plain. In Southern Africa a similar formation of granite is known as a koppie, a ...


Other uses

* Residual volume, the amount of air left in the lungs after a maximal exhalation; see
Lung volumes Lung volumes and lung capacities refer to the volume of air in the lungs at different phases of the respiratory cycle. The average total lung capacity of an adult human male is about 6 litres of air. Tidal breathing is normal, resting breathin ...


See also

* * Residue (disambiguation) {{disambiguation, math