On the partitioned matrix O A A * Q and its associated system A X = T , A * Y + Q X = Z
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 15 (1981) no. 2, p. 177-184
@article{M2AN_1981__15_2_177_0,
     author = {Valerio, Vladimiro},
     title = {On the partitioned matrix $\begin{pmatrix}O\&A\\A^\ast \&Q\end{pmatrix}$ and its associated system $AX=T, A^\ast Y+QX = Z$},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {15},
     number = {2},
     year = {1981},
     pages = {177-184},
     zbl = {0458.15003},
     mrnumber = {618822},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1981__15_2_177_0}
}
On the partitioned matrix $\begin{pmatrix}O&A\\A^\ast &Q\end{pmatrix}$ and its associated system $AX=T, A^\ast Y+QX = Z$. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 15 (1981) no. 2, pp. 177-184. http://www.numdam.org/item/M2AN_1981__15_2_177_0/

1 A Ben-Israel, A note on partitioned matrix equations SIAM Rev , 11 (1969), 247-250 | MR 245593 | Zbl 0175.02402

2 A Ben-Israel, Generalized inverses theory and applications J Wiley and Sons (1974), New York | MR 396607 | Zbl 0305.15001

3 P Bhimasankaram, On generalized inverse of partitioned matrices, Sankhya, Ser A, 33 (1971), 311-314 | Zbl 0231.15011

4 A Bjerhammar, Theory of errors and generalized inverse matrix Elsevir Scien Public Co (1973)

5 T Boullion, P L Odell, Generalized inverse matrices J Wiley and Sons (1971), New York | Zbl 0223.15002

6 F Burns, D Carlson, E Haynsworth, T Markham, A generalized inverse formula using the Schur complement, SIAM J , 26, (1974), 254-259 | MR 330181

7 D Carlson, E Haynsworth, T Markham, A generalization of the Schur complement by means of the Moore-Penrose Inverse SIAM J Appl Math 26 (1974), 169-175 | MR 347843 | Zbl 0245.15002

8 Ching-Hsiang Hung, T Markham, The Moore-Penrose inverse of a partitioned matrix M=ACBD Linear Alg and its Appl , 11 (1975), 73-86 | MR 369383 | Zbl 0326.15005

9 R E Cline, Representation for the generalized inverse of partitioned matrix SIAM J Appl Math , 12 (1964), 588-600 | MR 172890 | Zbl 0166.29902

10 R E Cline, Representation of generalized inverse of sums of matrices SIAM J Num Anal , Ser B, 2 (1965), 99-114 | Zbl 0142.26904

11 R W Cottle, Manifestation of the Schur complement Linear Alg and its Appl , 8 (1974), 189-211 | Zbl 0284.15005

12 T N E Greville, Some applications of the pseudo-inverse of a matrix SIAM Rev , 2 (1960), 15-22

13 C Hadley, Linear Algebra Addison-Wesley (1965), New York

14 G Marsaglia, G P H Styan, Rank conditions for generalized inverses of partitioned matrices Sankhya, Ser A (1974), 437-442 | MR 384827 | Zbl 0309.15002

15 G Marsaglia, Equations and inequalities for ranks of matrices Linear and Multil Alg , 2 (1974), 269-292 | Zbl 0297.15003

16 S K Mitra, P Bimasankharam, Generalized inverse of partitioned matrices and recalculation of least squares estimates for data or model charges Sankhya, Ser A, 33 (1971), 395-410 | MR 314208 | Zbl 0236.62049

17 S K Mitra, Fixed rank solutions of linear matrix equations Sankhya, Ser A, 34 (1971) 387-392 | MR 335545 | Zbl 0261.15008

18 C R Rao, Calculus of generalized inverses of matrices, Part I General Theory Sankhya, Ser A , 29 (1971), 317-342 | Zbl 0178.03103

19 C R Rao, S K Mitra, Generalized inverse of matrix and its application J Wiley and Sons (1971), New York

20 C H Rohde, Generalized inverse of partitioned matrices SIAM J , 13 (1965), 1033-1035 | MR 190161 | Zbl 0145.03801

21 V Valerio, Sulle inverse generalizzate e sulla soluzione di particolari sistemi di equazioni lineari, con applicazione al calcolo delle strutture reticolari Ace Naz Lincei, Rend sc , vol LX (1976), 84-89 | MR 460357 | Zbl 0361.15007

22 V Valerio, On the reticulated structures calculation Seminar held at the Delhi Campus of the Indian Statistical Institute (Nov 1977) unpublished communication, to appear