Open AccessThe associated Schur complements of M = [A B/C D]
Author(s) -
Hongxing Wang,
Xiaoji Liu
Publication year - 2011
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1101155w
Subject(s) - mathematics , schur complement , schur's theorem , pure mathematics , singular value , combinatorics , value (mathematics) , schur decomposition , statistics , eigenvalues and eigenvectors , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , physics , quantum mechanics
Let S1 = A ? BD?C and S2 = D?CA?B be the associated Schur complements of M = [A B/C D]. In this paper, we derive necessary and sufficient conditions for S1 = 0 imply S2 = 0 by using generalized inverses of matrices and singular value decompositions.