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  2. Spectrum (functional analysis) - Wikipedia

    en.wikipedia.org/wiki/Spectrum_(functional_analysis)

    In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix.

  3. Decomposition of spectrum (functional analysis) - Wikipedia

    en.wikipedia.org/wiki/Decomposition_of_spectrum...

    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.

  4. Spectrum of a matrix - Wikipedia

    en.wikipedia.org/wiki/Spectrum_of_a_matrix

    In mathematics, the spectrum of a matrix is the set of its eigenvalues. [ 1 ] [ 2 ] [ 3 ] More generally, if T : V → V {\displaystyle T\colon V\to V} is a linear operator on any finite-dimensional vector space , its spectrum is the set of scalars λ {\displaystyle \lambda } such that T − λ I {\displaystyle T-\lambda I} is not invertible .

  5. Spectral theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_theory

    The spectrum of T is the set of all complex numbers ζ such that R ζ fails to exist or is unbounded. Often the spectrum of T is denoted by σ(T). The function R ζ for all ζ in ρ(T) (that is, wherever R ζ exists as a bounded operator) is called the resolvent of T. The spectrum of T is therefore the complement of the resolvent set of T in ...

  6. Principles and Standards for School Mathematics - Wikipedia

    en.wikipedia.org/wiki/Principles_and_Standards...

    The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

  7. Eighth grade - Wikipedia

    en.wikipedia.org/wiki/Eighth_grade

    Eighth grade (also 8th Grade or Grade 8) is the eighth year of formal or compulsory education in the United States of America. The eighth grade is the second, (and typically final) year of middle school. Students in eighth grade are usually 13–14 years old. Different terms and numbers are used in other parts of the world.

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