Schrodinger flow is the Hamiltonian flow for energy functional on the space of maps from a Riemannian manifold into a Kahler manifold. I'll talk about some background on this flow, then focus on the special case of maps from a Euclidean space into the complex Grassmannian Gr(k,C^n). Terng and Uhlenbeck proved that Schrodinger flow of maps from R^1 into complex Grassmannian is gauge equivalent to the matrix nonlinear Schrodinger equation. Using this gauge equivalence and the result of Beals and Coifman, they obtained the global existence of Schrodinger flow with rapidly decay initial data. Applying the method of Terng and Uhlenbeck, we will see that Schrodinger flow of radial maps from R^m into the complex Grassmannian is gauge equivalent to a generalized matrix nonlinear Schrodinger equation. When the target is the 2-sphere, the gauge equivalence was studied by Lakshmanan and his colleagues by different method. They also observed that if the domain is R^2, then the corresponding matrix nonlinear Schrodinger equation is an integrable system.