The prospect of achieving quantum advantage with quantum neural networks (QNNs) is
exciting. Understanding how QNN properties (for example, the number of parameters M) …

In matrix theory, majorization plays a significant role. For instance, majorization relations
among eigenvalues and singular values of matrices produce a lot of norm inequalities and …

The aim of this book is to concisely present fundamental ideas, results, and techniques in
linear algebra and mainly matrix theory. The book contains ten chapters covering various …

Most books on linear operators are not easy to follow for students and researchers without
an extensive background in mathematics. Self-contained and using only matrix theory …

The main purpose of this monograph is to report on recent developments in the field of
matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other …

The restricted maximum likelihood (REML) estimates of dispersion parameters (variance
components) in a general (non-normal) mixed model are defined as solutions of the REML …

In the field of operator theory, an inequality due to LV Kantorovich provides an example of
“sailing upstream”, regarding the usual course of development of converse inequalities …

An operator means a bounded linear operator on a Hilbert space. This paper proves the
assertion made in its title. Theorem 1 yields the famous result that A≥ B≥ 0 assures Aα≥ …

A quote from the preface of the first edition:“Large-sample techniques provide solutions to
many practical problems; they simplify our solutions to difficult, sometimes intractable …

We study first-order optimization algorithms for computing the barycenter of Gaussian
distributions with respect to the optimal transport metric. Although the objective is …