A New Parametrization of Correlation Matrices

Rephasing invariant parametrization of flavor mixing matrices

A New Parametrization of Observers

This paper extends and generalizes recent results on the characterization and parametrization of observers for linear systems in the behavioral framework. We formulate the results in the language of quotient signal modules that was developed by Oberst and first used in the context of observer theory by the first author. The resulting characterization of observers in terms of a generalized inter...

On a Parametrization of Positive Semidefinite Matrices with Zeros

We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph. The images of the maps are convex cones, and the maps can only be surjecti...

On Rebonato and Jäckel’s Parametrization Method for Finding Nearest Correlation Matrices∗

Portfolio risk forecasts are often made by estimating an asset or factor correlation matrix. However, estimation difficulties or exogenous constraints can lead to correlation matrix candidates that are not positive semidefinite (psd). Therefore, practitioners need to reimpose the psd property with the minimum possible correction. Rebonato and Jäckel (2000) raised this question and proposed an a...

Correlation Matrices

In this paper we introduce the correlation matrix of a Boolean mapping, a useful concept in demonstrating and proving properties of Boolean functions and mappings. It is argued that correlation matrices are the “natural” representation for the proper understanding and description of the mechanisms of linear cryptanalysis [4]. It is also shown that the difference propagation probabilities and th...