Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Operator matrix”

Why Density Matrix (Operator)

Lei Ma · OSF Preprints (OSF Preprints) · 2013

Density Matrix is one of the most important concepts in QM. We can think of many reasons or advantages for density matrix. However, everyone can have a deeper understanding if we put our ideas together.

Cited by 0

Matrix and operator extensions

Hugo J. Woerdeman · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1989

In our contractive extension problem the operators again act on X = Y = c;n or on X = Y = 1 2 .But now the given part is of triangular form and consists of all diagonals below a given diagonal, the q -th say.The extensions are required to have operator norm matrices for I j -i I ~ q .Find the remaining matrices B ii, Ii -i I > q , such that the block matrix B = [ B Ii J ._ 11 is positive definite (shortly: B > 0).This problem was IJ=I introduced by H. Dym and I. Gohberg [23] who proved that a solution exists if and only if 1, ... ,n -q.(0.2)In a paper by J.A. Ball and I. Gohberg [5] a finite dimensional version of the shift invariant subspace approach of J.A. Ball and J.W. Helton [6] was used to derive a full parametrization of the set of all solutions via a linear fractional representation.The coefficients in this linear fractional map are determined using a theorem of Beurling-Lax type.In this book we shall present two other methods to obtain such a linear fractional representation and, moreover, we shall give explicit formulas for the coefficients in this linear fractional map in terms of the given data.The following two theorems are among our main results.THEOREM 0.1.Let B Ii = B ; 1 be given matrices for I j -i I ~ q ( ~ nl), and assume that condition (0.2) is satisfied.For 0 < j-i ~ q define the matrix Zu by where {j ii ,'Y iJ and r ii are given via the partitioning Put and let a 0 , , Aq be defined recursively by Put IJ i,j=I IJ iJ=I ' j ; i ; {3(j); , elsewhere; B = B2 B1 Bo ... . . . .such that Bi = Ai, IJ I ~ m, and the symbol of B is in the Wiener algebra.In this book we illustrate the band method only on the above mentioned examples.

Cited by 37Open access

Matrix Ordered Operator Algebras

Kate Juschenko, Stanislav Popovych · Chalmers Publication Library (Chalmers University of Technology) · 2007

We study the question when for a given *-algebra,A a sequence of cones C-n subset of M-n (A)(sa) can be realized as cones of positive operators in a faithful *-representation of A on a Hilbert space. We present a criterion analogous to Effros-Choi abstract characterization of operator systems. A characterization of operator algebras which are completely boundedly isomorphic to C*-algebras is also presented.

Cited by 0

Matrix Ordered Operator Algebras

Ekaterina Juschenko, Stanislav Popovych · arXiv (Cornell University) · 2007

We study the question when for a given *-algebra $\mathcal{A}$ a sequence of cones $C_n\in M_n(\mathcal{A})$ can be realized as cones of positive operators in a faithful *-representation of $\mathcal{A}$ on a Hilbert space. A characterization of operator algebras which are completely boundedly isomorphic to $C\sp*$-algebras is presented.

Cited by 0Open access

From Matrix to Operator Inequalities

Loring, Terry A. · arXiv (Cornell University) · 2009

We generalize Loewner's method for proving that matrix monotone functions are operator monotone. The relation x \leq y on bounded operators is our model for a definition for C*-relations of being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved, and verify a technical condition, then such a theorem will follow from its restriction to matrices. Applications are shown regarding norms of exponentials, the norms of commutators and "positive" noncommutative *-polynomials.

Cited by 0Open access

Symmetrization of operator matrix elements

Peter R. Taylor · International Journal of Quantum Chemistry · 1985

Abstract The method of Dupuis and King for generating matrix elements of a totally symmetric one‐electron operator in terms of symmetry‐distinct integrals only is generalized to the case of nontotally symmetric operators. For operators constructed from two‐electron integrals, explicit reduction of integral processing to permutationally inequivalent symmetry‐distinct integrals only is described, while for one‐electron operators further reductions are derived using double coset decompositions. Finally, some computational consequences of this approach are briefly discussed.

Cited by 16

Matrix and Operator Valued Functions

Israel Gohberg, L. A. Sakhnovich · Birkhäuser Basel eBooks · 1994

An operator approach to the Potapov scheme for the solution of interpolation problems . .

Cited by 20Open access

Gluonic Massive Operator Matrix Elements

Johannes Blümlein A, Er Hasselhuhn A, Sebastian Klein B et al. · 2012

The O(α 3 s nfT 2 F CA,F) terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable N using a new summation technique. These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series Heavy quark contributions to the deep inelastic scattering structure functions play a crucial role in the QCD analyses to determine the parton distribution functions and the strong coupling constant αs(M2 Z) in a consistent manner, cf. [1]. The heavy flavor corrections were calculated at NLO in semianalytic form in [2] 1. To avoid contributions of higher twist the analysis has to

Cited by 0

Hybrid Stabilizer Matrix Product Operator

Antonio Francesco Mello, Alessandro Santini, Mario Collura · Physical Review Letters · 2024

We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. By integrating these techniques, we enhance our ability to accurately model unitary dynamics while mitigating the exponential growth of entanglement encountered in classical simulations. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and random Clifford Floquet dynamics. This approach offers promising prospects for advancing our understanding of complex quantum phenomena and accelerating progress in quantum simulation.

Cited by 19

Physics-Informed Matrix Factorization Operator

Wenming Wu, Chenxi Tian, Licheng Jiao et al. · IEEE Transactions on Pattern Analysis and Machine Intelligence · 2025

Matrix factorization is a fundamental characterization model in machine learning and is usually solved using mathematical decomposition reconstruction loss. However, matrix factorization is a data-driven model whose results depend on data quality, making it susceptible to noise. Inspired by physics, the law of conservation of energy is used to introduce physical laws into matrix factorization, which is called Physics-informed Matrix Factorization operator (PiMF). The PiMF operator uses the heat conduction equation to construct the energy objective function for matrix factorization, thereby retaining the mathematical model's decomposition meaning and satisfying the interpretability of physics. The PiMF follows the physical laws, thereby suppressing irregular or sudden noise signals that violate these physical principles. The solutions of the PiMF operator include more comprehensive knowledge of mathematics and physics, which improves the ability to generalize complex data, especially for noisy data. We demonstrate the consistency of the energy objective function and the mathematical model, which verifies the feasibility of matrix factorization using physical energy laws. In addition, the physical interpretability of the PiMF operator is proved from the perspective of energy decline. This study proposes two practical algorithms for PiMF in classification and clustering tasks, enhancing the practicability of matrix factorization by incorporating task-specific prior information constraints. The experimental results of PiMF for classification and clustering demonstrate the advantages of the proposed operator. The importance of physics-informed matrix factorization is verified, especially for noisy data.

Cited by 0