This is the first paper of a two-long series in which we study linear generalized inverses that minimize matrix norms. Such generalized inverses are famously represented by the Moore-Penrose pseudoinverse (MPP) which happens to minimize the Frobenius norm. Freeing up the degrees of freedom associated with Frobenius optimality enables us to promote other interesting properties. In this Part I, w...

Hybrid beamforming provides a promising solution to achieve high data rate transmission at millimeter waves. To implement the hybrid beamforming at the transceiver, a common solution is to decouple the transmitter and receiver functions and then optimize them separately based on given channel state information. However, many references ignore the complexity of the high-dimensional channel estim...

structures on a model based on available prior informaAlgorithms are presented for least-squares approximation. Earlier work on these problems has primarily contion of Toeplitz and Hankel matrices from noise corsisted of using Singular Value Decomposition [4, 5, 81, rupted or ill-composed matrices, which may not have where only the rank information of the underlying sigcorrect structural or ran...

The nuclear norm (sum of singular values) of a matrix is often used in convex heuristics for rank minimization problems in control, signal processing, and statistics. Such heuristics can be viewed as extensions of l1-norm minimization techniques for cardinality minimization and sparse signal estimation. In this paper we consider the problem of minimizing the nuclear norm of an affine matrix val...

As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an m× n matrix with m ≤ n is 1/ √ m and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper, the smallest possible ratio between spectral and Frobenius norms of n1×· · ·×nd tensors of order d, also called the best rank-one approximation ratio i...

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

The problem of low-rank approximation with convex constraints, which often appears in data analysis, image compression and model order reduction, is considered. Given a data matrix, the objective is to find an approximation of desired lower rank that fulfills the convex constraints and minimizes the distance to the data matrix in the Frobenius-norm. The problem of matrix completion can be seen ...

Pseudo-Riemannian geometry and Hilbert–Schmidt norms are two important fields of research in applied mathematics. One the main goals this paper will be to find a link between these fields. In respect, present paper, we introduce analyze quantities pseudo-Riemannian geometry, namely H-distorsion and, respectively, Hessian χ-quotient. This second quantity investigated using Frobenius (Hilbert–Sch...