Abstract: First,design of optimal narrow band spatial matrix filters with specified passband response error and specified stopband response is concerned as well as the design of optimal matrix filter with minimum normalized total response error in passband and stopband.By using Lagrange multiplier theory,the optimal solutions are given,the equations for finding the optimal Lagrange multipliers are offered,the design efficiency is enhanced enormously.The design efficiency can be further enhanced by generalized singular value decomposition.Second,the influence of spatial matrix filter designed by using a specified frequency on other frequency's steering matrix is analyzed theoretically.The design of optimal broad band spatial matrix filter can be derived by it.Simulation shows that the proposed method can be used to design the broad band matrix filter with invariable“position”,“width”and“response”.