Dozens of machine learning algorithms require computing the inverse of a matrix. Computing a matrix inverse is conceptually easy, but implementation is one of the most challenging tasks in numerical ...

Abstract. In this paper, we present the explicit expression for the group inverse of the sum of two matrices. As an application, the explicit expression for the group ...

The extension problem for rectangular matrices with values in Banach algebra to an invertible square matrix is investigated. For this problem to be solvable for a matrix D, the following condition is ...

Theoretical physicists from Kavli IPMU have demonstrated that any non-invertible symmetry operation in theoretical physics is ...