Using The Finite Field Of Order N Idempotent Matrix Constructed Geometric Grid

Lattice is a kind of important partially ordered sets, its theory play an important role in many branches of mathematics.such as computer logical design and procedure theory.To construct some kinds of practical lattice is a very interesting work.In china,Wan., his students and cooperators construct geometric lattice by means of linear spaces,and discuss the geometric lattice that generated by various orbits or subspaces with the same dimension or rank under the action of classical groups over finite field.But the results on geometric lattice constructed by using matrices are very few.In the present paper,we construct geometric lattice with idempotent matrix.Some results on geometric lattice are involved in the present paper. Here we recall some definitions and facts from geometric lattice,and then by the method of decomposition form of idempotent matrix over a finite field,one geometric lattice is obtained. At the same time,the present paper compute the characteristic polynomial and the parameters that involved in the geometric lattice.