Integer Matrix Diagonalization

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...

Integer program with bimodular matrix

Let A be an m × n integral matrix of rank n. We say that A is bimodular if the maximum of the absolute values of the n×n minors is at most 2. We give a polynomial time algorithm that finds an integer solution for system Ax ≤ b. A polynomial time algorithm for integer program max{cx : Ax ≤ b} is constructed proceeding on some assumptions.

Sensitivity Analysis for the Problem of Matrix Joint Diagonalization

We investigate the sensitivity of the problem of Non-Orthogonal (matrix) Joint Diagonalization (NOJD). First, we consider the uniqueness conditions for the problem of Exact Joint Diagonalization (EJD), which is closely related to the issue of uniqueness in tensor decompositions. As a by-product, we derive the well-known identifiability conditions for Independent Component Analysis (ICA), based ...