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 …

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 …

Oct 23, 2013 · The discussion clarifies the distinctions between Hilbert spaces and Euclidean spaces, emphasizing that while Euclidean space is a finite-dimensional Hilbert space, not all …

Aug 11, 2023 · The forum discussion centers on the challenges of fully reading and understanding classic mathematical and theoretical physics texts, specifically "Morse & Feshbach" and …

Dec 26, 2013 · Riemannian manifolds can possess various positive definite metrics, and not all Riemannian manifolds qualify as Hilbert spaces. The conversation highlights the importance of …

May 11, 2019 · The following formulation in terms of 7 basic rules of quantum mechanics was agreed upon among the science advisors of Physics Forums.

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 …

Feb 20, 2017 · The discussion centers on the debate regarding whether David Hilbert can be considered the last universalist in mathematics, a title often attributed to Henri Poincaré. …

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 …

Mar 27, 2012 · A Hilbert space is defined as a complete inner product space, which means it possesses an inner product and every Cauchy sequence converges within it. Vector spaces …