Please use this identifier to cite or link to this item: https://doi.org/10.1137/080712945
Title: Inertia and rank characterizations of some matrix expressions
Authors: Chu, D. 
Hung, Y.S.
Woerdeman, H.J.
Keywords: Completion
Inertia
Matrix equation
Partial matrix
Rank
Issue Date: 2009
Citation: Chu, D., Hung, Y.S., Woerdeman, H.J. (2009). Inertia and rank characterizations of some matrix expressions. SIAM Journal on Matrix Analysis and Applications 31 (3) : 1187-1226. ScholarBank@NUS Repository. https://doi.org/10.1137/080712945
Abstract: In this paper we consider the admissible inertias and ranks of the expressions A - BXB* - CY C* and A - BXC* ± CX*B* with unknowns X and Y in the four cases when these expressions are: (i) complex self-adjoint, (ii) complex skew-adjoint, (iii) real symmetric, (iv) real skew symmetric. We also provide a construction for X and Y to achieve the desired inertia/rank that uses only unitary/orthogonal transformation, thus leading to a numerically reliable construction. In addition, we look at related block matrix completion problems [A ±B* ±C * B X ±E* C E Y] with either two diagonal unknown blocks and [A ±B* ±X * B D ±C* X C E] with an unknown off-diagonal block. Finally, we also provide all admissible ranks in the case when we drop any adjointness/symmetry constraint. © 2009 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Matrix Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/103418
ISSN: 08954798
DOI: 10.1137/080712945
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