Related papers: Equivalent matrices up to permutations

If $A$ is a tridiagonal matrix, then the equations $AX=I$ and $XA=I$ defining the inverse $X$ of $A$ are in fact the second order recurrence relations for the elements in each row and column of $X$. Thus, the recursive algorithms should be…

A $n\times n$ matrix $A$ has normal defect one if it is not normal, however can be embedded as a north-western block into a normal matrix of size $(n+1)\times (n+1)$. The latter is called a minimal normal completion of $A$. A construction…

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…

We study the transference through finite index extensions of the notion of equational coherence, as well as its effective counterpart. We deduce an explicit algorithm for solving the following algorithmic problem about size two integral…

$K$ is an algebraically closed field with characteristic $0$ and $f$ is a polynomial or a holomorphic function. We study all solutions of the equation $XA-AX=f(X)$, in the unknown $X\in M_n(K)$, when $A\in M_n(K)$ is diagonalizable.

We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…

In this paper, we describe non invertible matrix in GF(2)which can be used as multiplication matrix in Hill Cipher technique for one way hash algorithm. The matrices proposed are permutation matrices with exactly one entry 1 in each row and…

Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…

An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…

This paper studies a variant of the McEliece cryptosystem able to ensure that the code used as the public key is no longer permutation-equivalent to the secret code. This increases the security level of the public key, thus opening the way…

This note is concerned with the linear matrix equation $X = AX^\top B + C$, where the operator $(\cdot)^\top$ denotes the transpose ($\top$) of a matrix. The first part of this paper set forth the necessary and sufficient conditions for the…

Any permutation polynomial is an $ n $-cycle permutation. When $n$ is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These…

We consider the recovery of a nonnegative vector x from measurements y = Ax, where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when A corresponds to the adjacency matrix of a bipartite graph with sufficient…

We present a combination of the Mixed-Echelon-Hermite transformation and the Double-Bounded Reduction for systems of linear mixed arithmetic that preserve satisfiability and can be computed in polynomial time. Together, the two…

We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By…

We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method…

Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half…

We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…