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The Matrix Equations and Tensor Techniques IX (METTIX) Workshop will be hosted on Thursday and Friday 09-10 September 2021 in Perugia, Italy, at the Department of Mathematics and Computer Science. This is the ninth in a series of biennial appointments. As in previous meetings, the focus will be on recent theoretical and computational advances in the solution of tensor problems and linear and nonlinear matrix equations. The meeting will be held in a hybrid format (virtual and in-person).