Quantum matrix diagonalization visualized

Quantum Diagonalization of Hermitean Matrices

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to diagonalize hermitean (N × N) matrices by quantum mechanical measurements only. To do so, one considers the given matrix as an observable of a single spin wit...

Random Matrix Diagonalization—Some Numerical Computations

Simultaneous Matrix Diagonalization: the Overcomplete Case

Many algorithms for Independent Component Analysis rely on a simultaneous diagonalization of a set of matrices by means of a nonsingular matrix. In this paper we provide means to determine the matrix when it has more columns than rows.

Notes on basis changes and matrix diagonalization

Let V be an n-dimensional real (or complex) vector space. Vectors that live in V are usually represented by a single column of n real (or complex) numbers. Linear operators act on vectors and are represented by square n×n real (or complex) matrices. If it is not specified, the representations of vectors and matrices described above implicitly assume that the standard basis has been chosen. That...

Quantum state diffusion, density matrix diagonalization, and decoherent histories: A model.

We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival. The QSD picture exploits a mathematical connection between the usual Markovian master equation for the evolution of the density operator and a class of stochastic non-linear Schr...