Acronyms that contain the term generalized inverse 

Generalized inverse

In mathematics, and in particular, algebra, a generalized inverse of an element x is an element y that has some properties of an inverse element but not necessarily all of them. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A {\displaystyle A} . Formally, given a matrix A ∈ R n × m {\displaystyle A\in \mathbb {R} ^{n\times m}} and a matrix A g ∈ R m × n {\displaystyle A^{\mathrm {g} }\in \mathbb {R} ^{m\times n}} , A g {\displaystyle A^{\mathrm {g} }} is a generalized inverse of A {\displaystyle A} if it satisfies the condition A A g A = A . {\displaystyle AA^{\mathrm {g} }A=A.} The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse.

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