On the partitioned matrix O A A * Q and its associated system A X = T , A * Y + Q X = Z

Vladimiro Valerio

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1981)

  • Volume: 15, Issue: 2, page 177-184
  • ISSN: 0764-583X

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Valerio, Vladimiro. "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 15.2 (1981): 177-184. <http://eudml.org/doc/193375>.

@article{Valerio1981,
author = {Valerio, Vladimiro},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {partitioned matrix; generalized inverses; linear systems; existence, uniqueness and construction of solutions},
language = {eng},
number = {2},
pages = {177-184},
publisher = {Dunod},
title = {On the partitioned matrix $\begin\{pmatrix\}O&A\\A^\ast &Q\\ \end\{pmatrix\}$ and its associated system $AX=T,A^\ast Y+QX = Z$},
url = {http://eudml.org/doc/193375},
volume = {15},
year = {1981},
}

TY - JOUR
AU - Valerio, Vladimiro
TI - On the partitioned matrix $\begin{pmatrix}O&A\\A^\ast &Q\\ \end{pmatrix}$ and its associated system $AX=T,A^\ast Y+QX = Z$
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1981
PB - Dunod
VL - 15
IS - 2
SP - 177
EP - 184
LA - eng
KW - partitioned matrix; generalized inverses; linear systems; existence, uniqueness and construction of solutions
UR - http://eudml.org/doc/193375
ER -

References

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  3. 3 P BHIMASANKARAM, On generalized inverse of partitioned matrices, Sankhya, Ser A, 33 (1971), 311-314 Zbl0231.15011
  4. 4 A BJERHAMMAR, Theory of errors and generalized inverse matrix Elsevir Scien Public Co (1973) Zbl0267.65002
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  8. 8 CHING-HSIANG HUNG, T MARKHAM, The Moore-Penrose inverse of a partitioned matrix M = A C B D Linear Alg and its Appl , 11 (1975), 73-86 Zbl0326.15005MR369383
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  11. 11 R W COTTLE, Manifestation of the Schur complement Linear Alg and its Appl , 8 (1974), 189-211 Zbl0284.15005
  12. 12 T N E GREVILLE, Some applications of the pseudo-inverse of a matrix SIAM Rev , 2 (1960), 15-22 Zbl0168.13303
  13. 13 C HADLEY, Linear Algebra Addison-Wesley (1965), New York 
  14. 14 G MARSAGLIA, G P H STYAN, Rank conditions for generalized inverses of partitioned matrices Sankhya, Ser A (1974), 437-442 Zbl0309.15002MR384827
  15. 15 G MARSAGLIA, Equations and inequalities for ranks of matrices Linear and Multil Alg , 2 (1974), 269-292 Zbl0297.15003
  16. 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 Zbl0236.62049MR314208
  17. 17 S K MITRA, Fixed rank solutions of linear matrix equations Sankhya, Ser A, 34 (1971) 387-392 Zbl0261.15008MR335545
  18. 18 C R RAO, Calculus of generalized inverses of matrices, Part I General Theory Sankhya, Ser A , 29 (1971), 317-342 Zbl0178.03103
  19. 19 C R RAO, S K MITRA, Generalized inverse of matrix and its application J Wiley and Sons (1971), New York Zbl0236.15004
  20. 20 C H ROHDE, Generalized inverse of partitioned matrices SIAM J , 13 (1965), 1033-1035 Zbl0145.03801MR190161
  21. 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 Zbl0361.15007MR460357
  22. 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 

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