Dense Subspaces in Hermitean Spaces of Uncountable Dimensions
Author : Mikko Saarimäki
Publisher :
Page : 18 pages
File Size : 16,68 MB
Release : 1983
Category : Hermitian symmetric spaces
ISBN :
Author : Mikko Saarimäki
Publisher :
Page : 18 pages
File Size : 16,68 MB
Release : 1983
Category : Hermitian symmetric spaces
ISBN :
Author : Jean H Gallier
Publisher : World Scientific
Page : 760 pages
File Size : 26,47 MB
Release : 2024-06-21
Category : Mathematics
ISBN : 981129173X
The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.
Author : Jean H Gallier
Publisher : World Scientific
Page : 896 pages
File Size : 13,54 MB
Release : 2020-03-16
Category : Mathematics
ISBN : 9811216584
Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.
Author : Jean Gallier
Publisher : Springer Nature
Page : 627 pages
File Size : 45,45 MB
Release : 2020-08-18
Category : Mathematics
ISBN : 3030460479
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Author : Veikko T. Purmonen
Publisher :
Page : 100 pages
File Size : 34,24 MB
Release : 1986
Category : Boundary value problems
ISBN :
Author : Pekka Neittaanmäki
Publisher :
Page : 324 pages
File Size : 38,93 MB
Release : 1985
Category : Numerical analysis
ISBN :
Author : Jyväskylän yliopisto. Matematiikan laitos
Publisher :
Page : 358 pages
File Size : 42,30 MB
Release : 1987
Category : Mathematics
ISBN :
Author : Pekka Neittaanmäki
Publisher :
Page : 46 pages
File Size : 48,38 MB
Release : 1985
Category : Mathematical optimization
ISBN :
Author : Juha Heinonen
Publisher :
Page : 22 pages
File Size : 29,59 MB
Release : 1986
Category : Measure theory
ISBN :
Author : Timo Tiihonen
Publisher :
Page : 24 pages
File Size : 39,97 MB
Release : 1987
Category : Boundary value problems
ISBN :