Department of Mathematics
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The researches on the solvability conditions and the structural representations of solutions to matrix algebraic equations have been one of the active topics in algebra for a long time. In the past decades, matrix algebraic equations are widely used in many areas such as engineering, physics, system and control theory, computer science, and information science.

In this talk, we will focus on matrix algebraic equations over some non-commutative algebras which have very close relations with system and control theory and quantum computing. The main questions include the solvability conditions, general solutions, structural representations and extremal ranks of the solutions to some matrix algebraic equations and coupled generalized Sylvester matrix equations.