Tau functions of the constrained matrix KP hierarchy

The constrained matrix KP hierarchy $(L^k{)}_{<0}={\sum }_{i=1}^m{Q}_i{\mathrm{\partial }}^{-1}{R}_i^{⊺}$ is investigated from the aspects of tau functions. Firstly, the matrix KP hierarchy is viewed as one special reduction of the multi-component KP hierarchy. Then bilinear equations of the constrained matrix KP hierarchy as the multi-component KP hierarchy are given in terms of tau functions. Finally based upon these results, the tau functions for the constrained matrix KP hierarchy are constructed by using the multi-component boson-fermion correspondence. Notice that the solutions of the constrained matrix KP hierarchy are derived without using quasi-determinants.