Related papers: A Canonical Form for Positive Definite Matrices
This paper presents a new compact canonical-based algorithm to solve the problem of single-output completely specified NPN Boolean matching. We propose a new signature vector Boolean difference and cofactor (DC) signature vector. Our…
The main goal of this article is to study the existence of a unique positive definite common solution to a pair of matrix equations of the form \begin{eqnarray*} X^r=Q_1 + \displaystyle \sum_{i=1}^{m} {A_i}^*F(X)A_i \mbox{ and } X^s=Q_2 +…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…
We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
We propose a gradient-based Jacobi algorithm for a class of maximization problems on the unitary group, with a focus on approximate diagonalization of complex matrices and tensors by unitary transformations. We provide weak convergence…
For regular linear time-invariant DAEs the corresponding matrix pencil is regular and the computation of a standard canonical form is well-understood. Although the investigation of linear DAEs with time-varying coefficients is more complex,…
We characterize positive definiteness for some family of matrices. As an application we derive explicit value of the quadratic embedding constants of the path graphs.
On the basis of shell model simulations, it is conjectured that the Lanczos construction at fixed quantum numbers defines---within fluctuations and behaviour very near the origin---smooth canonical matrices whose forms depend on the rank of…
The purpose of this note is to give explicit criteria to determine whether a real generalized Cartan matrix is of finite type, affine type or of hyperbolic type by considering the principal minors and the inverse of the matrix. In…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the…
We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product.…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville…
Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…
We prove the existence of a canonical form for semi-deterministic transducers with incomparable sets of output strings. Based on this, we develop an algorithm which learns semi-deterministic transducers given access to translation queries.…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…