In this paper, we define the Moore–Penrose inverse of tensors with the Einstein product, and
the explicit formulas of the Moore–Penrose inverse of some block tensors are obtained. The …

We develop a novel approach based on the canonical correlation analysis to identify the
number of the global factors in the multilevel factor model. We propose the two consistent …

The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion of symmetric
real matrices with application in the graph theory. We introduce a novel concept of positively …

In order to extend the notation of the Moore–Penrose inverse from an operator with closed
range to a generalized Drazin invertible operator, we present a new generalized inverse …

The problem of best subset selection in linear regression is considered with the aim to find a
fixed size subset of features that best fits the response. This is particularly challenging when …

One important application of the Sherman–Morrison formula is the construction of an
efficient method for computing the inverse of an arrowhead matrix. Our intention is to apply …

We study the natural gradient method for learning in deep Bayesian networks, including
neural networks. There are two natural geometries associated with such learning systems …

A novel analytical model development and simulation of melt‐electrospinning process is
presented. Unconstrained equations of motion for the description of a discretized melt …

In this paper, we characterize complementable operators and provide more precise
expressions for the Schur complement of these operators using a single Douglas solution …

Abstract Let X∈ C m× m and Y∈ C n× n be nonsingular matrices, and let N∈ C m× n.
Explicit expressions for the Moore–Penrose inverses of M= XNY and a two-by-two block …