particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily...

1903. The terms pseudoinverse and generalized inverse are sometimes used as synonyms for the Moore–Penrose inverse of a matrix, but sometimes applied...

In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions...

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov...

\end{aligned}}} Some of the properties of inverse matrices are shared by generalized inverses (such as the Moore–Penrose inverse), which can be defined for any m-by-n...

In linear algebra, a constrained generalized inverse is obtained by solving a system of linear equations with an additional constraint that the solution...

semigroups generalize inverse semigroups, the unique element defined this way in a *-regular semigroup is called the generalized inverse or Moore–Penrose...

single-matrix SVD. The generalized singular value decomposition (GSVD) is a matrix decomposition on a pair of matrices which generalizes the singular value...

inverse function. The inverse function is also differentiable, and the inverse function rule expresses its derivative as the multiplicative inverse of...

Inverse element Inverse function, a function that "reverses" another function Generalized inverse, a matrix that has some properties of the inverse matrix...

that A or D is singular, substituting a generalized inverse for the inverses on M/A and M/D yields the generalized Schur complement. The Schur complement...

In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite...

}})}}}} where Σ + {\displaystyle {\boldsymbol {\Sigma }}^{+}} is the generalized inverse and det ∗ {\displaystyle \det \nolimits ^{*}} is the pseudo-determinant...

normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian distribution (GIG). Its probability density function (see...

percentile. Some useful properties of the inverse cdf (which are also preserved in the definition of the generalized inverse distribution function) are: F − 1...

set A left inverse function for a mapping between sets A kind of generalized inverse Left-cancellative Loop (algebra), an algebraic structure with identity...

In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix. Let A be a square matrix. The index of...

{b} } where A−1 is the inverse matrix of A. If A has no inverse, solutions—if any—can be found using its generalized inverse. Matrices and matrix multiplication...

(zero), but it can also refer to a more generalized zero element. In elementary mathematics, the additive inverse is often referred to as the opposite number...

invGauss, LaplacesDemon, and statmod. Generalized inverse Gaussian distribution Tweedie distributions—The inverse Gaussian distribution is a member of...

sufficiently large k. That is, it is the space of generalized eigenvectors (first sense), where a generalized eigenvector is any vector which eventually becomes...

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing...

mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if...

website of the University College London. Penrose, R. (1955). "A generalized inverse for matrices". Mathematical Proceedings of the Cambridge Philosophical...

science, an inverse-square law is any scientific law stating that the observed "intensity" of a specified physical quantity is inversely proportional...

inverse also readily generalizes to categories. An inverse category is simply a category in which every morphism f : X → Y has a generalized inverse g :...

In mathematics, the inverse Laplace transform of a function F {\displaystyle F} is a real function f {\displaystyle f} that is piecewise-continuous,...

a special case of the generalized gamma distribution, the generalized integer gamma distribution, and the generalized inverse Gaussian distribution....

Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates 1 x {\textstyle...

invertible, and if it is, its right inverse can differ from its left inverse. (See Generalized inverse § One-sided inverse.) Determinants are not defined over...