In this paper, some representations for the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors are found. Also, the invertibility for some linear combinations of commuting generalized and hypergeneralized projectors is considered.

The present work is devoted to deriving closed form expressions for the elements of Moore-Penrose inverse tridiagonal real skew-symmetric matrices. In first part we obtain results, concerning matrices even order. A calculation approach generalized inverses odd order provided.

The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.

In this paper, it is given equivalent conditions for the absorption laws in terms of the Moore-Penrose, group, core inverse, core inverse dual, {1}, {1,2}, {1,3}, and {1,4} inverses in rings. The results given here extend the results of [X. Liu, H. Jin, and D.S. Cvetković-Ilić. The absorption laws for the generalized inverses. Appl. Math. Comp., 219:2053–2059, 2012.].

Motivated by the representation for Moore-Penrose inverse of block matrix over a *-regular ring presented in [R.E. Hartwig and P. Patr?cio, When does flip? Operators Matrices, 6(1):181-192, 2012], we show that formula is same as expression given [Nieves Castro-Gonz?lez, Jianlong Chen Long Wang, Further results on generalized inverses rings with involution, Elect. J. Linear Algebra, 30:118-134, ...