act on local Hilbert spaces, and form an algebra over the complex field. Based on this, the package provides the following features: Unitcell Description Framework: The Hamiltonian can be constructed ...

In high school, I studied mathematics quite a lot. I opened Chart-style reference books, solved problem sets, and competed for scores on mock exams. But looking back now, I have a strange feeling.

using Diagonalizations, PosDefManifold, Test n, t=10, 100 # generate an nxt data matrix X=genDataMatrix(n, t) # principal component analysis pX=pca(X) # the following is an equivalent constructor ...

Abstract: A fast algorithm, named Complex-Valued Fast Frobenius DIAGonalization (CVFFDIAG), is proposed for seeking the nonunitary approximate joint diagonalizer of a given set of complex-valued ...

Electricity powers our lives, including our cars, phones, computers, and more, through the movement of electrons within a circuit. While we can't see these electrons, electric currents moving through ...

Japan now hosts the world’s most advanced quantum–classical hybrid setup, pairing IBM’s cutting-edge quantum system with one of Earth’s fastest supercomputers. On Tuesday, IBM and Japan’s national ...

ABSTRACT: A modal identification algorithm is developed, combining techniques from Second Order Blind Source Separation (SOBSS) and State Space Realization (SSR) theory. In this hybrid algorithm, a ...

This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set ...

Dynamic complex matrix equation (DCME) is frequently encountered in the fields of mathematics and industry, and numerous recurrent neural network (RNN) models have been reported to effectively find ...

Abstract: This paper introduces a new algorithm to approximate non-orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of ...