On the relation between Moore's and Penrose's conditions
Moore (1920) defined the reciprocal of any matrix over the complex field by three conditions, but the beauty of the definition was not realized until Penrose (1955) defined the same inverse using four conditions. The reciprocal is now often called the Moore-Penrose inverse, and has been widely used...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007317 |
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| Summary: | Moore (1920) defined the reciprocal of any matrix over
the complex field by three conditions, but the beauty of the
definition was not realized until Penrose (1955) defined the same
inverse using four conditions. The reciprocal is now often called
the Moore-Penrose inverse, and has been widely used in
various areas. This note comments on the definitions of
Moore-Penrose inverse, and gives a new characterization for two
types of weak Moore-Penrose inverses, which exposes an
important relation between Moore's and Penrose's
conditions. It also attempts to emphasize the merit of Moore's
definition, which has been overlooked mainly due to Moore's
unique notation. Two examples are given to demonstrate some
combined applications of Moore's and Penrose's conditions,
including a correction for an incorrect proof of Ben-Israel's
(1986) characterization for Moore's conditions. |
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| ISSN: | 0161-1712 1687-0425 |