  This paper proposes matrix-scaled consensus algorithm, which generalizes the
scaled consensus algorithm in \cite{Roy2015scaled}. In (scalar) scaled
consensus algorithms, the agents' states do not converge to a common value, but
to different points along a straight line in the state space, which depends on
the scaling factors and the initial states of the agents. In the matrix-scaled
consensus algorithm, a positive/negative definite matrix weight is assigned to
each agent. Each agent updates its state based on the product of the sum of
relative matrix scaled states and the sign of the matrix weight. Under the
proposed algorithm, each agent asymptotically converges to a final point
differing with a common consensus point by the inverse of its own scaling
matrix. Thus, the final states of the agents are not restricted to a straight
line but are extended to an open subspace of the state-space. Convergence
analysis of matrix-scaled consensus for single and double-integrator agents are
studied in detail. Simulation results are given to support the analysis.
