Several problems in mathematics can be viewed as completion problems. Matrix theory is particularly rich in such problems. Such problems nicely blend graph theoretic notions with matrix theory. In this chapter we consider one particular completion problem, the positive definite completion problem, in detail.
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References and Further Reading
A. Berman and N. Shaked-Monderer, Completely Positive Matrices, World Scientific, Singapore, 2003.
M. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
R. Grone, C.R. Johnson, E.M. Sá and H. Wolkowitz, Positive definite completions of partial hermitian matrices, Linear Algebra Appl., 58:109–124 (1984).
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(2010). Positive Definite Completion Problem. In: Graphs and Matrices. Universitext. Springer, London. https://doi.org/10.1007/978-1-84882-981-7_11
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DOI: https://doi.org/10.1007/978-1-84882-981-7_11
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