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spectral theorem

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  • Spectral theorem — In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a …   Wikipedia

  • Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

  • Spectral theory — In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix. The name was introduced by David Hilbert in his original formulation of Hilbert space theory, which was… …   Wikipedia

  • Spectral efficiency — Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is… …   Wikipedia

  • Spectral method — Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain Dynamical Systems, often involving the use of the Fast Fourier Transform. Where applicable, spectral methods have… …   Wikipedia

  • Spectral radius — In mathematics, the spectral radius of a matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum, which is sometimes denoted by rho;( middot;).pectral radius of a matrixLet lambda;1, hellip;,… …   Wikipedia

  • Spectral theory of compact operators — In functional analysis, compact operators are linear operators that map bounded sets to precompact ones. Compact operators acting on a Hilbert space H is the closure of finite rank operators in the uniform operator topology. In general, operators …   Wikipedia

  • Spectral density — In statistical signal processing and physics, the spectral density, power spectral density (PSD), or energy spectral density (ESD), is a positive real function of a frequency variable associated with a stationary stochastic process, or a… …   Wikipedia

  • Spectral graph theory — In mathematics, spectral graph theory is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of its adjacency matrix or Laplacian matrix. An undirected graph has a symmetric adjacency …   Wikipedia

  • Spectral phase interferometry for direct electric-field reconstruction — In ultrafast optics, spectral phase interferometry for direct electric field reconstruction (SPIDER) is an ultrashort pulse measurement technique.The basicsSPIDER is an interferometric ultrashort pulse measurement technique in the frequency… …   Wikipedia

  • Spectral asymmetry — In mathematics and physics, the spectral asymmetry is the asymmetry in the distribution of the spectrum of eigenvalues of an operator. In mathematics, the spectral asymmetry arises in the study of elliptic operators on compact manifolds, and is… …   Wikipedia

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