The matrix completion problem asks to describe the properties of matrices, obtained as completions of given matrices with some missing entries. The problem is important due to its applications in many areas, such as moment problems, real algebraic geometry, big data analysis, etc. In the diploma thesis we focus on the study of possible inertia of completions of special hermitian matrices. Using tools from linear algebra we show, that all possible inertia are parametrized by the integer points within the inertia polytope. We present the connection between special matrices and chordal graphs and use it to derive a formula for more efficient computation of inertia. We also implement the algorithms for the computation of the inertia polytope and the inertia of special matrices and present them on numerical examples.
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