Particular formulae for the Moore-Penrose inverse of a columnwise partitioned matrix
J. K. Baksalary1 , O. M. Baksalary2
1 Faculty of Mathematics, Informatics and Econometrics, Zielona Góra University, ul. Podgorna 50, 65-246 Zielona Góra, Poland
2 Institute of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
Linear Algebra and Its Applications, 421, 16-23 (2007)
An essential part of Cegielski's [Linear Algebra Appl. 335 (2001) 167] considerations of some properties of Gram matrices with nonegative inverses, which are pointed out to be crucial in constructing obtuse cones, consists in developing some particular formulae for the Moore-Penrose inverse A+ of a columnwise partitioned matrix A = (A1 : A2) under the assumption that it is of full column rank. In the present paper, these results are generalized by weakening the assumption mentioned above to the requirement that the ranges of A1 and A2 are disjoint.