Normed vector spaces

Part 1 of ebook "Measure, integration and real analysis" provides readers with contents including: chapter 1 - Riemann integration; chapter 2 - Measures; chapter 3 - Integration; chapter 4 - Differentiation; chapter 5 - Product measures; chapter 6 - Banach spaces;...

211p tieulangtran 28-09-2023 8 2   Download

Part 1 of ebook "Applied linear algebra (Second edition)" has presents the following content: Chapter 1 - Linear algebraic systems; Chapter 2 - Vector spaces and bases; Chapter 3 - Inner products and norms; Chapter 4 - Orthogonality; Chapter 5 - Minimization and least squares;...

325p dieptieuung 20-07-2023 7 3   Download

Legendre-Fenchel duality plays a helpful role in convex optimization. Herein, we introduce some overview of Legendre-Fenchel duality, with an eye toward later applications in nonlinear elasticity. The basic tool here is functional analysis.

3p viputrajaya2711 22-06-2020 14 0   Download

We point out the equivalence of the fact that every norm on a vector space is a restriction of an order-unit norm to that of Paulsen’s construction concerning generalization of operator systems.

3p danhdanh27 07-01-2019 23 1   Download

This is the second volume containing examples from Functional analysis. The topics here are limited to Topological and metric spaces, Banach spaces and Bounded operators. Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

96p sn_buon 29-11-2012 57 8   Download

Hilbert Spaces 1.1 Inner product spaces Example 1.1 Prove that in a real vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2, and in a complex vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2 + i x + iy2 + i x − iy2. These are the so-called polarization identities. They tell us that in a Hilbert space, the inner product is determined by the norm.

109p sn_buon 29-11-2012 51 4   Download

A Class of Normalised Algorithms for Online Training of Recurrent Neural Networks A normalised version of the real-time recurrent learning (RTRL) algorithm is introduced. This has been achieved via local linearisation of the RTRL around the current point in the state space of the network. Such an algorithm provides an adaptive learning rate normalised by the L2 norm of the gradient vector at the output neuron. The analysis is general and also covers simpler cases of feedforward networks and linear FIR filters...

12p doroxon 12-08-2010 89 15   Download