Author/Authors :
Yongge Tian، نويسنده , , George P. H. Styan، نويسنده ,
Abstract :
We establish several rank equalities for idempotent and involutary matrices. In particular, we obtain new formulas for the rank of the difference, the sum, the product and the commutator of idempotent or involutary matrices. Extensions to scalar-potent matrices are also included. Our matrices are complex and are not necessarily Hermitian.
Keywords :
Rank additivity , Rank equality , Partitioned matrix , Rank inequality , Rank of a difference , Rank of a product , Rank of a sum , Ranksubtractivity , Commutator , Scalar-potent matrix , Generalized inverse , Idempotent matrix , Involutory matrix , Oblique projector , Commutativity , Schur complement , Rank of the commutator , Orthogonal projector
