Related papers: Construction, classification and parametrization o…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
While convolution and self-attention mechanisms have dominated architectural design in deep learning, this survey examines a fundamental yet understudied primitive: the Hadamard product. Despite its widespread implementation across various…
A closed formula multiallelic Walsh (or Hadamard) transform is introduced. Basic results are derived, and a statistical interpretation of some of the resulting linear forms is discussed.
For a given selection of rows and columns from a Fourier matrix, we give a number of tests for whether the resulting submatrix is Hadamard based on the primitive sets of those rows and columns. In particular, we demonstrate that whether a…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
We introduce numerical characteristics of Sylvester and Hadamard matrices and give their estimates and some of their applications.
In this paper, we define the phases of a complex sectorial matrix to be its canonical angles, which are uniquely determined from a sectorial decomposition of the matrix. Various properties of matrix phases are studied, including those of…
Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard…
A partial Hadamard matrix is a matrix $H\in M_{M\times N}(\mathbb T)$ whose rows are pairwise orthogonal. We associate to each such $H$ a certain quantum semigroup $G$ of quantum partial permutations of $\{1,...,M\}$ and study the…
We axiomatize and study the matrices of type $H\in M_N(A)$, having unitary entries, $H_{ij}\in U(A)$, and whose rows and columns are subject to orthogonality type conditions. Here $A$ can be any $C^*$-algebra, for instance $A=\mathbb C$,…
This is the Habilitation Thesis manuscript presented at Besan\c{c}on on January 5, focusing on Matrix Analysis, Matrix Inequalities and Matrix Decompositions. There are also some topics in (Hilbert space) Operator Theory. The text should be…
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…
The main aim of the present note is to prove new Hadamard like integral inequalities for the product of the convex functions.
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al.…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
Complex Hadamard matrices have received considerable attention in the past few years due to their appearance in quantum information theory. While a complete characterization is currently available only up to order 5 (in \cite{haagerup}),…
This is an expository paper which presents the holomorphic classification of rational complex surfaces from a simple and intuitive point of view, which is not found in the literature. Our approach is to compare this classification with the…
In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize…
Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…