A Family of Maximal Mathieu Subspaces of Matrix Algebras

Let $F$ be a field. In this note we give a construction for a family of maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras $M_n(F)$ $(n\ge 2)$. As an application we also give a classification of Mathieu subspaces of $M_2(F)$ under the condition that $F$ is algebraically closed.

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