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...

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

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

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

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

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...

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

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...

number 0, 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...

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

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

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...

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...

a formula for the derivative of the inverse function. In multivariable calculus, this theorem can be generalized to any continuously differentiable, vector-valued...

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

distribution Generalized inverse Gaussian distribution Generalized least squares Generalized linear array model Generalized linear mixed model Generalized linear...

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

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...

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

{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...

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

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

arbitrarily small. This iteration can also be generalized to a wider sort of inverses; for example, matrix inverses. Every real or complex number excluding...

natural numbers. Absorbing element Additive inverse Generalized inverse Identity (equation) Identity function Inverse element Monoid Pseudo-ring Quasigroup...

RGA is often generalized in practice to be used when G {\displaystyle \mathrm {G} } is singular, e.g., non-square, by replacing the inverse of G {\displaystyle...

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

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