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SubmittedCC BY-NC-ND V4.0, Open
Journal article
INERTIA AND RANK CHARACTERIZATIONS OF SOME MATRIX EXPRESSIONS
SIAM journal on matrix analysis and applications, v 31(3), pp 1187-1226
01 Jan 2009
Abstract
In this paper we consider the admissible inertias and ranks of the expressions A - BXB* - CYC* 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
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with either two diagonal unknown blocks and
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with an unknown off-diagonal block. Finally, we also provide all admissible ranks in the case when we drop any adjointness/symmetry constraint.
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Details
- Title
- INERTIA AND RANK CHARACTERIZATIONS OF SOME MATRIX EXPRESSIONS
- Creators
- Delin Chu - matchudl@nus.edu.sgY. S. Hung - yshung@hkueee.hku.hkHugo J. Woerdeman - Drexel University
- Publication Details
- SIAM journal on matrix analysis and applications, v 31(3), pp 1187-1226
- Publisher
- Siam Publications
- Number of pages
- 40
- Grant note
- DMS-0500678 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000271800100019
- Scopus ID
- 2-s2.0-72449170482
- Other Identifier
- 991019168671804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied