Informasjon om | Engelsk ordet EIGENVALUES

Eksempler på bruk av EIGENVALUES i en setning

• Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.
• In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
• Any invertible matrix can be uniquely represented according to the polar decomposition as the product of a unitary matrix and a hermitian matrix with positive eigenvalues.
• However this last fact can be proved in an elementary way as follows: the eigenvalues of a real skew-symmetric matrix are purely imaginary (see below) and to every eigenvalue there corresponds the conjugate eigenvalue with the same multiplicity; therefore, as the determinant is the product of the eigenvalues, each one repeated according to its multiplicity, it follows at once that the determinant, if it is not 0, is a positive real number.
• The eigenvalues and eigenvectors of Hermitian matrices play a crucial role in analyzing signals and extracting meaningful information.
• It also numerically calculated the eigenvalues of a two-electron atom quantum system based on programming by Yigal Accad who put Pekeris' development of the relevant equations into machine code.
• From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity).
• 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.
• In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
• The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
• The Schläfli matrix is useful because its eigenvalues determine whether the Coxeter group is of finite type (all positive), affine type (all non-negative, at least one zero), or indefinite type (otherwise).
• The eigenfunctions corresponding to non-zero eigenvalues are continuous on X and K has the representation.
• The diagonal entries of the normal form are the eigenvalues (of the operator), and the number of times each eigenvalue occurs is called the algebraic multiplicity of the eigenvalue.
• Spectral theory, in mathematics, a theory that extends eigenvalues and eigenvectors to linear operators on Hilbert space, and more generally to the elements of a Banach algebra.
• Correlating statistical descriptions of eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system).
• Geometric multiplicities of eigenvalues (but not the eigenspaces, which are transformed according to the base change matrix P used).
• In addition, looking at a system from the point of view of frequency can often give an intuitive understanding of the qualitative behavior of the system, and a revealing scientific nomenclature has grown up to describe it, characterizing the behavior of physical systems to time varying inputs using terms such as bandwidth, frequency response, gain, phase shift, resonant frequencies, time constant, resonance width, damping factor, Q factor, harmonics, spectrum, power spectral density, eigenvalues, poles, and zeros.
• Similarly, the QR algorithm is used to compute the eigenvalues of any given matrix, which are the diagonal entries of the upper triangular matrix of the Schur decomposition.
• However, the case of a compact operator on a Hilbert space (or Banach space) is still tractable, since the eigenvalues are at most countable with at most a single limit point λ = 0.
• While these operators may not be compact, their inverses (when they exist) may be, as in the case of the wave equation, and these inverses have the same eigenfunctions and eigenvalues as the original operator (with the possible exception of zero).

Forberedelse av siden tok: 358,05 ms.