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The spectrum of T restricted to H ac is called the absolutely continuous spectrum of T, σ ac (T). The spectrum of T restricted to H sc is called its singular spectrum, σ sc (T). The set of eigenvalues of T is called the pure point spectrum of T, σ pp (T). The closure of the eigenvalues is the spectrum of T restricted to H pp.
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as follows from Brown's representability theorem .
Khanmigo is a chatbot powered by GPT-4 technology, designed to assist users with mathematics, science, humanities, and coding inquiries, as well as aiding in learning these subjects. It incorporates the large language model of OpenAI. Khan Academy introduced Khanmigo on March 14, 2023. [35] [36] Users can have access [37] for $4 per month ...
The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
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A pair of graphs are said to be cospectral mates if they have the same spectrum, but are non-isomorphic. The smallest pair of cospectral mates is {K 1,4, C 4 ∪ K 1}, comprising the 5-vertex star and the graph union of the 4-vertex cycle and the single-vertex graph [1].
The spectrum in a rainbow. A spectrum (pl.: spectra or spectrums) [1] is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word spectrum was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism.