Preface MATRICES: Basic Properties of Vectors and Matrices Kronecker Products, the Vec-Operator and the Moore- Penrose Inverse Miscellaneous Matrix Results DIFFERENTIALS: THE THEORY: Mathematical Preliminaries Differentials and Differentiability The Second Differential Static Optimization DIFFERENTIALS: THE PRACTICE: Some Important Differentials First- Order Differentials and Jacobian Matrices Second-Order Differentials and Hessian Matrices INEQUALITIES: Inequalities THE LINEAR MODEL: Statistical Preliminaries The Linear Regression Model Further Topics in the Linear Model APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: Maximum Likelihood Estimation Simultaneous Equations Topics in Psychometrics Subject Index Bibliography.

Matrix Differential Calculus with Applications in Statistics and Econometrics

The paper introduces a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices. The results of the paper naturally extend techniques based on singular values and eliminate their most serious difficulties.

Analysis of feedback systems with structured uncertainties

Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications References Index.

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The Convenient Setting of Global Analysis

Characterization of the subdifferential of some matrix norms

Constrained optimization of the receiver's output variance has previously been proposed as a relatively simple method for designing blind multiuser detectors for DS-CDMA systems. A single constraint is sufficient for the AWGN case, whereas multiple constraints should be used in a multipath environment. It is shown in this paper that the choice of the constraint parameters in the multipath case can have a significant effect on the system performance. A max/min approach for optimizing the constraint is proposed, resulting in blind solutions with improved performance. It is shown that the performance of the proposed method tends to be close to that of the MMSE receiver at high SNR, whereas the constraint parameters converge to the multipath channel parameters. The proposed method does not require knowledge of the interfering users' codes and timing. Simulation results support those performance claims.

B. J. Berkowitz

Papers

Perturbation theory of eigenvalue problems