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On some properties of saddle point matrices with vector blocks. (English) Zbl 1138.90017

Summary: The paper is concerned with the saddle point type problem, often called KKT system in optimization literature, which arises in a wide variety of applications. Some properties of saddle point matrices with two vector blocks, connected with the standard quadratic program over the standard simplex, if the matrix block is symmetric, or game theory, if the matrix block is not necessarily symmetric are revisited and discussed. Conditions of nonsingularity of these block matrices, and proper-ties related to determinant, rank or inertia are investigated as well.

MSC:

90C20 Quadratic programming
15A63 Quadratic and bilinear forms, inner products
15A24 Matrix equations and identities
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