Abstract Extending an approach considered by Radjawi and Rosenthal (2002), we investigate the set of square matrices whose square equals a linear combination of the matrix itself and an idempotent matrix. Special attention is paid to the Moore-Penrose and group inverse of matrices belonging to this set. References: Radjavi, H. and P. Rosenthal (2002). On… (More)

The article of Ding and Pye [3] is reconsidered and extended. In contrast to their assertion, we find that the Sherman-Morrison formula is well suited to prove certain statements about a class of bordered matrices.

A new metric for subspaces of a finite dimensional vector space V is identified. The metric is determined by the dimensions of M + N and M∩N , where M and N are subspaces of V . Some properties of the metric are derived as well. 2000 Mathematics Subject Classification: 15A03

Representing two orthogonal projectors on a finite dimensional vector spaces (i.e., Hermitian idempotent matrices) as partitioned matrices turns out to be very powerful tool in considering properties of such a pair. The usefulness of this representation is discussed and several new characterizations of a pair of orthogonal projectors are provided, with… (More)