The invertibility of the difference and the sum of commuting generalized and hypergeneralized projectors

Abstract

In this article, we study necessary and sufficient conditions for the invertibility of a linear combination c ₁ A ^k  + c ₂ B ^l , in the case when A and B are both commuting generalized or hypergeneralized projectors. We present some results relating different matrix partial orderings and the invertibility of a linear combination c ₁ A ^k  + c ₂ B ^l when A and B are hypergeneralized projectors.

Keywords:

• idempotent
• projector
• generalized projector
• hypergeneralized projector

AMS Subject Classification:

• 15A09

Acknowledgements

Authors are supported by Grant No. 174007 of the Ministry of Science and Technological Development, Republic of Serbia.