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On completions of symmetric and antisymmetric block diagonal partial matrices. (English) Zbl 1283.15081

Summary: A partial matrix is a matrix where only some of the entries are given. We determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum rank of the antisymmetric completions of an antisymmetric partial matrix where only the diagonal blocks are given.

MSC:

15A83 Matrix completion problems
15A03 Vector spaces, linear dependence, rank, lineability
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[1] Bostian, A. A.; Woerdeman, H. J., Unicity of minimal rank completions for tri-diagonal partial block matrices, Linear Algebra Appl., 325, 1-3, 23-55 (2001) · Zbl 0988.15004
[2] Brualdi, R. A.; Huang, Z.; Zhan, X., Singular, nonsingular and bounded rank completions of ACI-matrices, Linear Algebra Appl., 433, 7, 1452-1462 (2010) · Zbl 1205.15042
[3] Cain, B. E., The inertia of a Hermitian matrix having prescribed diagonal blocks, Linear Algebra Appl., 37, 173-180 (1981) · Zbl 0462.15009
[4] Cain, Bryan E.; Marques de Sʼa, E., The inertia of a Hermitian matrix having prescribed complementary principal submatrices, Linear Algebra Appl., 37, 161-171 (1981) · Zbl 0456.15011
[5] Cohen, N.; Johnson, C. R.; Rodman, Leiba; Woerdeman, H. J., Ranks of completions of partial matrices, (The Gohberg Anniversary Collection, vol. I. The Gohberg Anniversary Collection, vol. I, Calgary, AB, 1988. The Gohberg Anniversary Collection, vol. I. The Gohberg Anniversary Collection, vol. I, Calgary, AB, 1988, Oper. Theory Adv. Appl., vol. 40 (1989), Birkhäuser: Birkhäuser Basel), 165-185
[6] Fiedler, M.; Markham, T. L., Rank-preserving diagonal completions of a matrix, Linear Algebra Appl., 85, 49-56 (1987) · Zbl 0607.15002
[7] Geelen, J. F., Maximum rank matrix completion, Linear Algebra Appl., 288, 1-3, 211-217 (1999) · Zbl 0933.15026
[8] McTigue, J.; Quinlan, R., Partial matrices whose completions have ranks bounded below, Linear Algebra Appl., 435, 9, 2259-2271 (2011) · Zbl 1225.15025
[9] Tian, Y., Completing block Hermitian matrices with maximal and minimal ranks and inertias, Electron. J. Linear Algebra, 21, 124-141 (2010) · Zbl 1207.15029
[10] Woerdeman, H. J., Minimal rank completions for block matrices, Linear Algebra and Applications. Linear Algebra and Applications, Valencia, 1987. Linear Algebra and Applications. Linear Algebra and Applications, Valencia, 1987, Linear Algebra Appl., 121, 105-122 (1989) · Zbl 0681.15002
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