Author
Franz Rellich
Bio: Franz Rellich is an academic researcher. The author has contributed to research in topics: Poincaré–Lindstedt method & Eigenvalues and eigenvectors. The author has an hindex of 5, co-authored 6 publications receiving 646 citations.
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Book•
01 Apr 1988
TL;DR: In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.
Abstract: 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.
2,868 citations
DOI•
01 Nov 1982TL;DR: In this article, a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices is introduced, which naturally extend techniques based on singular values and eliminate their most serious difficulties.
Abstract: 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.
1,987 citations
Book•
30 Sep 1997TL;DR: Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly real compact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifold, infinite dimensional differential geometry Manifolds of Mappings Further applications References as mentioned in this paper.
Abstract: 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.
1,291 citations
493 citations
TL;DR: In this article, a characterization of the subdifferential of matrix norms from two classes, orthogonally invariant norms and operator (or subordinate) norms, is given for some special cases.
429 citations