Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\). (English) Zbl 0957.15002
The authors establish a basic representation and a representation theorem for the outer inverse \(A^{(2)}_{T,S}\) of a matrix \(A\), which is the matrix \(X\) satisfying
\[
XAX=X,\;R(X)=T\text{ and }N(X)=S.
\]
Several specific representations and iterative methods for \(A^{(2)}_{T,S}\) are given. The paper shows that this representation includes many of the traditional generalized inverses and outer inverses, and the relation of the results to these outer inverses will be explored.
Reviewer: Rodica Covaci (Cluj-Napoca)
MSC:
| 15A09 | Theory of matrix inversion and generalized inverses |
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
Keywords:
generalized inverses; limit representation; Neumann expansion; representation; outer inverse; iterative methodsReferences:
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