Related papers: Twists of two or multiple idempotent matrices
Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a…
In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome and hard to compute, theoretical methods: (1) average Hamiltonian theory following…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
In this paper, two kinds of generalizations of ideal matrices, generalized ideal matrices and double ideal matrices. are obtained and studied, The concepts of generalized ideal matrices and double ideal matrices are proposed, and their…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of…
We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the…
We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric…
In this paper, we give a complete self-contained proof that the rigidity matrix of a symmetric bar and joint framework (as well as its transpose) can be transformed into a block-diagonalized form using techniques from group representation…
Using the decomposition of semimagic squares into the associated and balanced symmetry types as a motivation, we introduce an equivalent representation in terms of block-structured matrices. This block representation provides a way of…
We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…
We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address the generic minimal rank problem.
We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues…
Toeplitz matrices are ubiquitous and play important roles across many areas of mathematics. In this paper, we present some algebraic results concerning block Toeplitz matrices with block entries belonging to a commutative algebra $\AA$. The…
In this paper, we develop a geometric framework for matrix rank-metric codes based on generator tensors and their slice spaces. To every nondegenerate matrix rank-metric code, we associate two systems, which translate metric properties of…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…