Learn the Basics of Hilbert Spaces and Their Relatives: Definitions
Feb 16, 2018 · Hilbert spaces are at first real or complex vector spaces, or are Hilbert spaces. So all the theorems and definitions of linear algebra apply to the finite-dimensional ones and many to the …
What Distinguishes Hilbert Spaces from Euclidean Spaces?
Oct 23, 2013 · Hilbert spaces are not necessarily infinite dimensional, I don't know where you heard that. Euclidean space IS a Hilbert space, in any dimension or even infinite dimensional. A Hilbert space is …
Derivation of the Einstein-Hilbert Action Abstract Most people justify the form of the E-H action by saying that it is the simplest scalar possible. But simplicity, one can argue, is a somewhat subjective and ill …
Why is Hilbert not the last universalist? • Physics Forums
Feb 20, 2017 · The discussion revolves around the characterization of mathematicians Hilbert and Poincaré as universalists, specifically questioning why Hilbert is not considered the last universalist …
Verifying Inner Product & Showing $\ell^ {2}$ is a Hilbert Space
Apr 26, 2013 · The discussion revolves around verifying the inner product in the space \ (\ell^ {2}\) and demonstrating that it is a Hilbert Space. The original poster presents a sequence of real numbers …
Difference between hilbert space,vector space and manifold?
Mar 27, 2012 · A Hilbert space is a vector space with a defined inner product. This means that in addition to all the properties of a vector space, I can additionally take any two vectors and assign to …
Why are Hilbert spaces used in quantum mechanics?
May 27, 2016 · Some participants suggest that Hilbert spaces are used in quantum mechanics due to the non-commutative nature of observables and the requirement for operators to act on states. …
Where does the Einstein-Hilbert action come from?
Nov 21, 2010 · The Hilbert action comes from postulating that gravity comes from making the metric dynamical, and that the dynamical equations come from an action, which is a scalar. There are more …
The History and Importance of the Riemann Hypothesis
May 21, 2022 · David Hilbert and Pólya György had already noticed that the Riemann hypothesis would follow if the zeros were eigenvalues of an operator where is a Hermitian (i.e. self-adjoint) operator, …
Learn the Basics of Hilbert Spaces and Their Relatives: Operators
Mar 6, 2018 · The fact that the definition of Hilbert spaces doesn’t include any requirement on dimensionality is important here, although they are primarily meant to investigate infinite-dimensional …