Asymptotic diagonalization of matrix systems

Matrix commutators: their asymptotic metric properties and relation to approximate joint diagonalization

We analyze the properties of the norm of the commutator of two Hermitian matrices, showing that asymptotically it behaves like a metric, and establish its relation to joint approximate diagonalization of matrices, showing that almost-commuting matrices are almost jointly diagonalizable, and vice versa. We show an application of our results in the field of 3D shape analysis.

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...

On asymptotic stability of Prabhakar fractional differential systems

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given.