On column and null spaces of functions of a pair of oblique projectors
O. M. Baksalary1 , G. Trenkler2
1 Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, PL 61-614 PoznaĹ„, Poland
2 Department of Statistics, Dortmund University of Technology, Vogelpothsweg 87, D-44221 Dortmund, Germany
Linear and Multilinear Algebra, 61,1116-1129 (2013)
The paper provides an extensive investigation of a pair of vectors spaces, with a particular attention paid to perpendicular subspaces. Several new properties of the pair are identified, some of which enabled to derive known facts about subspaces by means of simpler proofs. The approach utilized exploits partitioned representations of orthogonal projectors and is based on the fact that there is one-to-one correspondence between an orthogonal projector and the subspace onto which it projects.