What does generalized inverse mean?
Definitions for generalized inverse
gen·er·al·ized in·verse
This dictionary definitions page includes all the possible meanings, example usage and translations of the word generalized inverse.
Wikipedia
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.
Numerology
Chaldean Numerology
The numerical value of generalized inverse in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of generalized inverse in Pythagorean Numerology is: 9
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"generalized inverse." Definitions.net. STANDS4 LLC, 2024. Web. 1 May 2024. <https://www.definitions.net/definition/generalized+inverse>.
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