Related papers: Structured matrices and inverses
In this article one-sided (b, c)-inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In adddition, the (b, c)-inverse and the inverse along an element will be also…
Perturbation theory plays a crucial role in sensitivity analysis, which is extensively used to assess the robustness of numerical techniques. To quantify the relative sensitivity of any problem, it becomes essential to investigate…
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the…
We show that a structural matrix algebra $A$ is isomorphic to the endomorphism algebra of an algebraic-combinatorial object called a generalized flag. If the flag is equipped with a group grading, an algebra grading is induced on $A$. We…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
The objective of this manuscript is to understand the structure of an invertible linear map on the space of real symmetric matrices $\mathcal{S}^n$ that leaves invariant the closed convex cones of copositive and completely positive matrices…
This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries…
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…
We introduce ballot matrices, a signed combinatorial structure whose definition naturally follows from the generating function for labeled interval orders. A sign reversing involution on ballot matrices is defined. We show that matrices…
Idempotent elements play a fundamental role in ring theory, as they encode significant information about the underlying algebraic structure. In this paper, we study idempotent matrices from two perspectives. First, we analyze the partially…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal…
The matrix rank and its positive versions are robust for small approximations, i.e. they do not decrease under small perturbations. In contrast, the multipartite tensor rank can collapse for arbitrarily small errors, i.e. there may be a gap…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may…
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix $A\in\mathbb{F}^{N\times N}$ and a vector $b$, it is known that in the worst case $\Theta(N^2)$ operations over $\mathbb{F}$ are needed to…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…