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group inverse

Let $A$ be an $n\times n$ matrix over $\mathbb{R}$ . A group inverse for $A$ is an $n\times n$ matrix $X$ such that

	$\displaystyle AXA$	$\displaystyle=A$		(1)
	$\displaystyle XAX$	$\displaystyle=X$		(2)
	$\displaystyle AX$	$\displaystyle=XA.$		(3)

Such a matrix, when it exists, is unique and is denoted by $A^{\#}$ . A group inverse is a special case of a Drazin inverse.

Title	group inverse
Canonical name	GroupInverse
Date of creation	2013-03-22 17:01:17
Last modified on	2013-03-22 17:01:17
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	5
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 15A09