A unified approach to generalized inverses of linear operators: II. Extremal and proximal properties

Authors:
M. Z. Nashed and G. F. Votruba

Journal:
Bull. Amer. Math. Soc. **80** (1974), 831-835

MSC (1970):
Primary 47A50, 47A99, 41A50; Secondary 54C60, 54C65

DOI:
https://doi.org/10.1090/S0002-9904-1974-13529-9

Part I:
Bull. Amer. Math. Soc., Volume 80, Number 5 (1974), 825--830

MathSciNet review:
0365191

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References | Similar Articles | Additional Information

**1.**P. J. Erdelsky,*Projections in a normed linear space and a generalization of the pseudoinverse*, Doctoral Dissertation, California Institute of Technology, Pasadena, Calif., 1969.**2.**I. Erdelyi and A. Ben-Israel,*Extremal solutions of linear equations and generalized inversion between Hilbert spaces*, J. Math. Anal. Appl. 39 (1972), 298-313. MR**310680****3.**R. B. Holmes,*A course on optimization and best approximation*, Lecture Notes in Math., vol. 257, Springer-Verlag, Berlin, 1972. MR**420367****4.**M. Z. Nashed,*Generalized inverses, normal solvability, and iteration for singular operator equations*, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970), Academic Press, New York, 1971, pp. 311-359. MR 43 #1003. MR**275246****5.**M. Z. Nashed and G. F. Votruba,*A unified approach to generalized inverses of linear operators*: I.*Algebraic, topological, and projectional properties*, Bull. Amer. Math. Soc. 80 (1974), 825-830. MR**365190****6.**T. G. Newman and P. L. Odell,*On the concept of a p-q generalized inverse of a matrix*, SIAM J. Appl. Math. 17 (1969), 520-525. MR 41 #220. MR**255559****7.**R. Penrose,*On best approximate solutions of linear matrix equations*, Proc. Cambridge Philos. Soc. 52 (1956), 17-19. MR 17, 536. MR**74092****8.**C. R. Rao and S. K. Mitra,*Generalized inverse of matrices and its applications*, Wiley, New York, 1971. MR**338013**

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13529-9