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Notice on the Chipman generalization of the matrix inverse. (English) Zbl 0964.65043
The Chipman generalized inverse of an $$m\times n$$ real matrix $$A$$ is the unique matrix $$A^+_{MN}$$ that solves the minimum norm least squares problem with respect to the norms associated to the real positive definite matrices $$N$$ and $$M$$ in the domain and range, respectively. If instead of positive definite one has positive semidefinite matrices, uniqueness is no longer valid, and it is possible to exhibit a family of generalized inverses of $$A$$ that still solve the minimum norm least squares problem. The scope of the paper is to give a new proof showing this.

##### MSC:
 65F20 Numerical solutions to overdetermined systems, pseudoinverses 15A09 Theory of matrix inversion and generalized inverses
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##### References:
 [1] Chipman J. S.: On least squares with insufficient observations. J. Amer. Statist. Assoc. 59 (1964), 1078-1111. · Zbl 0144.42401 · doi:10.2307/2282625 [2] Rao C. R., Mitra K. S.: Generalized Inverse of Matrices and Its Application. J. Wiley, New York 1971. · Zbl 0236.15004
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