Generalized Inverses of Block Triangular Matrices
Carl Dean Meyer · SIAM Journal on Applied Mathematics · 1970
Previous article Next article Generalized Inverses of Block Triangular MatricesCarl D. Meyer, Jr.Carl D. Meyer, Jr.https://doi.org/10.1137/0119075PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Randall E. Cline, Representations for the generalized inverse of a partitioned matrix, J. Soc. Indust. Appl. Math., 12 (1964), 588–600 10.1137/0112050 MR0172890 0166.29902 LinkISIGoogle Scholar[2] M. J. Englefield, The commuting inverses of a square matrix, Proc. Cambridge Philos. Soc., 62 (1966), 667–671 MR0197486 0158.03501 CrossrefISIGoogle Scholar[3] Ivan Erdélyi, On the matrix equation $Ax=\lambda Bx$, J. Math. Anal. Appl., 17 (1967), 119–132 MR0202734 0153.04902 CrossrefISIGoogle Scholar[4] Carl D. Meyer, Jr., Generalized inverses of triangular matrices, SIAM J. Appl. Math., 18 (1970), 401–406 10.1137/0118034 MR0257100 0192.36701 LinkISIGoogle Scholar[5] C. D. Meyer and , R. J. Painter, Note on a least squares inverse for a matrix, J. Assoc. Comput. Mach., 17 (1970), 110–112 MR0274467 0206.32002 CrossrefISIGoogle Scholar[6] Carl D. Meyer, Jr., Representations for $(1)$- and $(1,\,2)$-inverses for partitioned matrices, Linear Algebra and Appl., 4 (1971), 221–232 10.1016/0024-3795(71)90017-6 MR0281724 0217.05403 CrossrefGoogle Scholar[7] M. H. Pearl, On generalized inverses of matrices, Proc. Cambridge Philos. Soc., 62 (1966), 673–677 MR0197485 0158.03502 CrossrefISIGoogle Scholar[8] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[9] Hans Schwerdtfeger, Introduction to Linear Algebra and the Theory of Matrices, P. Noordhoff, Groningen, 1950, 280–, The Netherlands MR0038923 0040.29503 Google Scholar[10] N. S. Urquhart, The nature of the lack of uniqueness of generalized inverse matrices, SIAM Rev., 11 (1969), 268–271 10.1137/1011044 MR0246890 0177.04903 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Magneto-Inertial Data Sensory Fusion Based on Jacobian Weighted-Left-Pseudoinverse18 July 2020 Cross Ref Sensory Fusion of Magnetoinertial Data Based on Kinematic Model With Jacobian Weighted-Left-Pseudoinverse and Kalman-Adaptive GainsIEEE Transactions on Instrumentation and Measurement, Vol. 68, No. 7 Cross Ref On Moore–Penrose inverses of quasi-Kronecker structured matricesLinear Algebra and its Applications, Vol. 436, No. 3 Cross Ref On regularity of block triangular fuzzy matricesJournal of Applied Mathematics and Computing, Vol. 16, No. 1-2 Cross Ref Completing triangular block matrices with maximal and minimal ranksLinear Algebra and its Applications, Vol. 321, No. 1-3 Cross Ref On schur complements in an ep matrixPeriodica Mathematica Hungarica, Vol. 16, No. 3 Cross Ref Schur complements and statisticsLinear Algebra and its Applications, Vol. 36 Cross Ref Computational methods of linear algebraJournal of Soviet Mathematics, Vol. 15, No. 5 Cross Ref Annotated Bibliography on Generalized Inverses and Applications Cross Ref Roth’s equivalence problem in unit regular rings1 January 1976 | Proceedings of the American Mathematical Society, Vol. 59, No. 1 Cross Ref Generalized Inverses and Ranks of Block MatricesCarl D. Meyer,Jr.12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 25, No. 4AbstractPDF (397 KB)Representations for (1)- and (1,2)-inverses for partitioned matricesLinear Algebra and its Applications, Vol. 4, No. 3 Cross Ref Volume 19, Issue 4| 1970SIAM Journal on Applied Mathematics History Submitted:13 January 1970Published online:12 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119075Article page range:pp. 741-750ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics