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Monotone linear relations play important roles in variational inequalityproblems and quadratic optimizations. In this paper, we give explicit maximallymonotone linear subspace extensions of a monotone linear relation in finitedimensional spaces. Examples are provided to illustrate our extensions. Ourresults generalize a recent result by Crouzeix and Anaya.

Maximally Monotone Linear Subspace Extensions of Monotone Subspaces: Explicit Constructions and Characterizations