Constitution of Linear Combinations of Idempotent Matrices and its Properties

Constructing linear combinations of idempotent matrices is one of important issues. This paper firstly proposes the definition of n - by - n idempotent matrix of k. Then, the conditions that linear combination of idempotent matrix is idempotent matrix are proposed, also by using these properties, constructing method of idempotent matrix is given. Finally, the power of linear combination of idempotent matrix is discussed.