Dear editor,rnConsensus turns out to be an important paradigm in coordination of multi-agent systems [1].Previous studies largely concentrate on consensus problem over networks where the weights on edges are scalars, which cannot completely characterize the correlation of different dimensions corresponding to the state of an agent in the network.In fact, matrixvalued weights naturally arise when characterizing the interaction between a pair of agents in multi-agent networks,such as generalized electrical networks where currents, voltages, and resistances take matrix values [2, 3], opinion dynamics of multiple related topics in social network analysis [4], the observability problems for an array of coupled LC oscillators [5], and the consensus problems over matrixvalued weighted networks [6].Therefore, the matrix-valued weighted networks provide a natural extension of scalarvalued weighted networks, allowing characterizing more elaborate mutual interactions.