On the entries of orthogonal projection matrices

Authors:

• Oskar Maria Baksalary,
• Götz Trenkler

Abstract

The present paper is concerned with characterizing entries of orthogonal projectors (i.e., a Hermitian idempotent matrices). On the one hand, several bounds for the values of the entries are identified. On the other hand, particular attention is paid to the question of how an orthogonal projector changes when its entries are modified. The modifications considered are those of a single entry and of an entire row or column. Some applications of the results in the linear regression model are pointed out as well