November 2022

Moore-Penrose inverse of linear operators in Hilbert space

In this paper, we investigate properties of  with closed range satisfying the operator equations   In particular, we investigate the invertibility of   with closed range where the Moore-Penrose inverse of T turns out to be the usual inverse of T under some classes of operators. We also deduce the Moore-Penrose inverse of a perturbed linear operator  with closed range where  such...

Author(s): J. M. Mwanzia, M. Kavila and J. M. Khalagai  

November 2022

Division by zero in real and complex number arithmetic and some of its implications

In this paper, an attempt is made to include division by zero in ordinary arithmetic. Counting or measuring is done to get the value of multiples, powers, quotients, sums and differences of zeros. Zero divided by zero is taken to be equal to one. There are many infinities and many zeroes. The biggest of all infinities cannot be imagined and the smallest zero cannot be imagined also. An attempt is made to define a...

Author(s): Chihoro Ernest Tafadzwa