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Longer titles found: Eigenvalues and eigenvectors of the second derivative (view)

searching for Eigenvalues and eigenvectors 68 found (144 total)

alternate case: eigenvalues and eigenvectors

EISPACK (246 words) [view diff] exact match in snippet view article find links to article

EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating

Frobenius covariant (594 words) [view diff] exact match in snippet view article find links to article

polynomials of it, namely projection matrices Ai associated with the eigenvalues and eigenvectors of A.: pp.403, 437–8 They are named after the mathematician

Vera Kublanovskaya (684 words) [view diff] exact match in snippet view article find links to article

problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important

Spectral expansion solution (176 words) [view diff] exact match in snippet view article find links to article

vector is expressed directly (not as a transform) in terms of eigenvalues and eigenvectors of a matrix polynomial. Chakka, R. (1998). "Spectral expansion

Rössler attractor (3,602 words) [view diff] exact match in snippet view article find links to article

fixed points can be analyzed by determining their respective eigenvalues and eigenvectors. Beginning with the Jacobian: ( 0 − 1 − 1 1 a 0 z 0 x − c ) {\displaystyle

Spectral graph theory (1,838 words) [view diff] no match in snippet view article find links to article

of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency

Simple rational approximation (715 words) [view diff] exact match in snippet view article find links to article

secular functions. A divide-and-conquer algorithm to find the eigenvalues and eigenvectors for various kinds of matrices is well known in numerical analysis

Johnson graph (1,283 words) [view diff] no match in snippet view article find links to article

In mathematics, Johnson graphs are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph J ( n , k ) {\displaystyle

Modal analysis using FEM (701 words) [view diff] exact match in snippet view article find links to article

those seen in eigensystems. The physical interpretation of the eigenvalues and eigenvectors which come from solving the system are that they represent the

Jacobi eigenvalue algorithm (4,671 words) [view diff] exact match in snippet view article find links to article

algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization)

Arnoldi iteration (1,842 words) [view diff] exact match in snippet view article find links to article

of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing

Sylvester's formula (1,118 words) [view diff] exact match in snippet view article find links to article

function f(A) of a matrix A as a polynomial in A, in terms of the eigenvalues and eigenvectors of A. It states that f ( A ) = ∑ i = 1 k f ( λ i ) A i ,

Voigt effect (3,522 words) [view diff] exact match in snippet view article find links to article

effective dielectric tensor from which one calculates systems eigenvalues and eigenvectors. As usual, from this tensor, magneto-optical phenomena are described

Exceptional point (765 words) [view diff] exact match in snippet view article find links to article

singularities in the parameter space where two or more eigenstates (eigenvalues and eigenvectors) coalesce. These points appear in dissipative systems, which

Dyall Hamiltonian (490 words) [view diff] exact match in snippet view article find links to article

like the true Hamiltonian inside the CAS space, having the same eigenvalues and eigenvectors of the true Hamiltonian projected onto the CAS space. Dyall,

Kernel principal component analysis (1,338 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \lambda } and a {\displaystyle \mathbf {a} } are the eigenvalues and eigenvectors of K {\displaystyle K} . Then to normalize the eigenvectors a

Validated numerics (1,339 words) [view diff] exact match in snippet view article find links to article

computed eigenvalues and eigenvectors. Numerische Mathematik, 34(2), 189-199. Yamamoto, T. (1982). Error bounds for computed eigenvalues and eigenvectors. II

Canonical analysis (597 words) [view diff] exact match in snippet view article find links to article

analysis, each with its characteristic set of commonalities, eigenvalues and eigenvectors. Canonical analysis is a multivariate technique which is concerned

Spectrum of a matrix (510 words) [view diff] exact match in snippet view article find links to article

canonical form whereby the matrix is represented in terms of its eigenvalues and eigenvectors. The spectral radius of a square matrix is the largest absolute

Discrete Fourier transform (12,379 words) [view diff] exact match in snippet view article find links to article

doi:10.1109/29.1519. J. H. McClellan; T. W. Parks (1972). "Eigenvalues and eigenvectors of the discrete Fourier transformation". IEEE Transactions on

Quantum Fisher information (4,474 words) [view diff] exact match in snippet view article find links to article

\lambda _{k}} and | k ⟩ {\displaystyle \vert k\rangle } are the eigenvalues and eigenvectors of the density matrix ϱ , {\displaystyle \varrho ,} respectively

SLATEC (373 words) [view diff] exact match in snippet view article find links to article

differential equations (Runge–Kutta methods and similar) EISPACK 71 yes eigenvalues and eigenvectors FFTPACK 48 yes fast Fourier transform FISHPACK 19 yes use cyclic

Riemann invariant (1,430 words) [view diff] exact match in snippet view article find links to article

matrix a {\displaystyle \mathbf {a} } from the analysis above the eigenvalues and eigenvectors need to be found. The eigenvalues are found to satisfy λ 2 −

Quantum chaos (4,340 words) [view diff] exact match in snippet view article find links to article

quantum mechanics in non-perturbative regimes is to find the eigenvalues and eigenvectors of a Hamiltonian of the form H = H s + ε H n s , {\displaystyle

Circular ensemble (1,005 words) [view diff] exact match in snippet view article find links to article

doi:10.1063/1.1703863. V.L. Girko (1985). "Distribution of eigenvalues and eigenvectors of orthogonal random matrices". Ukrainian Mathematical Journal

Harmonic analysis (1,634 words) [view diff] exact match in snippet view article find links to article

and the integer multiples are known as harmonics. Study of the eigenvalues and eigenvectors of the Laplacian on domains, manifolds, and (to a lesser extent)

Google matrix (1,796 words) [view diff] exact match in snippet view article find links to article

Fig.6 from ). Arnoldi iteration method allows to compute many eigenvalues and eigenvectors for matrices of rather large size [13]. Other examples of G {\displaystyle

Beresford Parlett (832 words) [view diff] exact match in snippet view article find links to article

; Reinsch, C. (1969). "Balancing a matrix for calculation of eigenvalues and eigenvectors". Numerische Mathematik. 13 (4): 293–304. doi:10.1007/BF02165404

Mathcad (1,285 words) [view diff] exact match in snippet view article find links to article

constructs;[clarification needed] Vector and matrix operations, including eigenvalues and eigenvectors; Curve fitting and regression analysis; Statistical and design

Control reconfiguration (1,383 words) [view diff] exact match in snippet view article find links to article

conditions. In eigenstructure assignment, the nominal closed loop eigenvalues and eigenvectors (the eigenstructure) is recovered to the nominal case after a

Quadratic eigenvalue problem (999 words) [view diff] exact match in snippet view article find links to article

A-\lambda B} ), and solve a generalized eigenvalue problem. Once eigenvalues and eigenvectors of the linear problem have been determined, eigenvectors and

Expectation value (quantum mechanics) (1,912 words) [view diff] exact match in snippet view article

mechanics. This operator has a completely continuous spectrum, with eigenvalues and eigenvectors depending on a continuous parameter, x {\displaystyle x} . Specifically

Spin chain (1,138 words) [view diff] exact match in snippet view article find links to article

_{i}^{(n)}} . The central problem is then to determine the spectrum (eigenvalues and eigenvectors in H {\displaystyle {\mathcal {H}}} ) of the Hamiltonian. This

Elliptic operator (2,089 words) [view diff] exact match in snippet view article find links to article

L+\mu I:L^{2}(U)\rightarrow L^{2}(U)} admits a compact inverse. Eigenvalues and eigenvectors: If A is symmetric, bi,c are zero, then (1) Eigenvalues of L

Computational chemistry (8,349 words) [view diff] exact match in snippet view article find links to article

Kohn-Sham matrix. The diagonalization step, which finds the eigenvalues and eigenvectors of the matrix, contributes most to this scaling. Recent advances

Françoise Chatelin (605 words) [view diff] exact match in snippet view article find links to article

Her doctoral dissertation, Numerical methods for calculating eigenvalues and eigenvectors of a linear operator, was directed by Noël Gastinel. The University

Energy condition (2,326 words) [view diff] exact match in snippet view article find links to article

conditions is that they are essentially restrictions on the eigenvalues and eigenvectors of the matter tensor. A more subtle but no less important feature

Numerical linear algebra (2,507 words) [view diff] exact match in snippet view article find links to article

numerical problems have no direct solution; in order to find the eigenvalues and eigenvectors of an arbitrary matrix, we can only adopt an iterative approach

Phase plane (1,231 words) [view diff] exact match in snippet view article find links to article

orthogonal eigenvector to generate the second solution. Complex eigenvalues and eigenvectors generate solutions in the form of sines and cosines as well as

List of numerical libraries (2,660 words) [view diff] exact match in snippet view article find links to article

EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for

Exact solutions in general relativity (3,323 words) [view diff] exact match in snippet view article find links to article

conditions, which are similar to placing restrictions on the eigenvalues and eigenvectors of a linear operator. On the one hand, these conditions are far

Spectral theory (4,668 words) [view diff] exact match in snippet view article find links to article

useful examples about the combinatorial significance of the eigenvalues and eigenvectors in symmetric matrices, especially for the Rayleigh quotient with

Determining the number of clusters in a data set (2,750 words) [view diff] exact match in snippet view article find links to article

decomposition of the kernel matrix. It will then analyze the eigenvalues and eigenvectors to obtain a measure of the compactness of the input distribution

Divide-and-conquer eigenvalue algorithm (1,856 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T={\begin{bmatrix}T_{1}&0\\0&T_{2}\end{bmatrix}}.} The eigenvalues and eigenvectors of T {\displaystyle T} are simply those of T 1 {\displaystyle

Schrieffer–Wolff transformation (2,124 words) [view diff] exact match in snippet view article find links to article

with the chosen effective Hamiltonian to compute, for instance, eigenvalues and eigenvectors. In physics, this would generate effective low- (or high-)energy

Matrix differential equation (2,732 words) [view diff] exact match in snippet view article find links to article

_{1}+Be^{\lambda _{2}t}\mathbf {\hat {v}} _{2}.} Substituting the values of eigenvalues and eigenvectors yields [ x y ] = A e t [ 2 1 ] + B e − 5 t [ 1 2 ] . {\displaystyle

Bra–ket notation (6,315 words) [view diff] exact match in snippet view article find links to article

Ket space 2. Bra space 3. Operators 4. The outer product 5. Eigenvalues and eigenvectors Robert Littlejohn, Lecture notes on "The Mathematical Formalism

Stokes parameters (4,348 words) [view diff] exact match in snippet view article find links to article

coefficients in a linear combination of the Stokes operators. The eigenvalues and eigenvectors of the operator can be calculated from the polarization ellipse

Lane–Emden equation (3,443 words) [view diff] exact match in snippet view article find links to article

= 0 {\displaystyle dV/d\log \xi =dU/d\log \xi =0} ) and the eigenvalues and eigenvectors of the Jacobian matrix are tabulated below. Emden–Chandrasekhar

N-electron valence state perturbation theory (3,299 words) [view diff] exact match in snippet view article find links to article

like the true Hamiltonian inside the CAS space, having the same eigenvalues and eigenvectors of the true Hamiltonian projected onto the CAS space. Also, given

Dynamic mode decomposition (3,791 words) [view diff] exact match in snippet view article find links to article

v_{N}\}} . Regardless of the approach, the output of DMD is the eigenvalues and eigenvectors of A {\displaystyle A} , which are referred to as the DMD eigenvalues

Dynamical system (7,150 words) [view diff] exact match in snippet view article find links to article

under the action of the map. As in the continuous case, the eigenvalues and eigenvectors of A determine the structure of phase space. For example, if

Shear wave splitting (4,485 words) [view diff] exact match in snippet view article find links to article

equation (5) is left. Thus, To obtain the solution of (8), the eigenvalues and eigenvectors of matrix Γ j k {\displaystyle \Gamma _{jk}} are needed, which

Space-time adaptive processing (2,884 words) [view diff] exact match in snippet view article find links to article

applies principal component analysis to estimate the dominant eigenvalues and eigenvectors, and then applies a covariance taper and adds an estimated noise

Timeline of mathematics (7,795 words) [view diff] exact match in snippet view article find links to article

Kublanovskaya independently develop the QR algorithm to calculate the eigenvalues and eigenvectors of a matrix. 1961 – Stephen Smale proves the Poincaré conjecture

Hans Bethe (7,548 words) [view diff] exact match in snippet view article find links to article

Bethe ansatz, a method for finding the exact solutions for the eigenvalues and eigenvectors of certain one-dimensional quantum many-body models. He was influenced

Visual servoing (4,026 words) [view diff] exact match in snippet view article find links to article

information) giving an axis of rotation and the angle (by computing the eigenvalues and eigenvectors of the homography). The translational information is obtained

Discrete Laplace operator (5,719 words) [view diff] exact match in snippet view article find links to article

Kronecker sum of discrete Laplacians, in which case all its eigenvalues and eigenvectors can be explicitly calculated. In this approach, the domain is

Elliptic boundary value problem (3,615 words) [view diff] exact match in snippet view article find links to article

… . {\displaystyle j=1,2,\dots \,.} If one has computed the eigenvalues and eigenvectors, then one may find the "explicit" solution of L u = f {\displaystyle

Lagrangian coherent structure (10,246 words) [view diff] exact match in snippet view article find links to article

{\displaystyle S(x,t)} , and hence an LCS approach depending only on the eigenvalues and eigenvectors of S ( x , t ) {\displaystyle S(x,t)} is automatically frame-invariant

Hyperelastic material (6,926 words) [view diff] exact match in snippet view article find links to article

of solids, Springer, p. 157. Fox & Kapoor, Rates of change of eigenvalues and eigenvectors, AIAA Journal, 6 (12) 2426–2429 (1968) Friswell MI. The derivatives

Harris affine region detector (7,040 words) [view diff] exact match in snippet view article find links to article

SIFT descriptor. As discussed with the Harris detector, the eigenvalues and eigenvectors of the second-moment matrix, M = μ ( x , Σ I , Σ D ) {\displaystyle

Hückel method (7,291 words) [view diff] exact match in snippet view article find links to article

ethylene, shown in detail above, though we must now find the eigenvalues and eigenvectors of a 4 × 4 Hamiltonian matrix. We first write the molecular orbital

Kosambi–Karhunen–Loève theorem (10,711 words) [view diff] exact match in snippet view article find links to article

{1}{(k-{\frac {1}{2}})^{2}\pi ^{2}}}.} Proof In order to find the eigenvalues and eigenvectors, we need to solve the integral equation: ∫ a b K W ( s , t )

Quantum computational chemistry (3,351 words) [view diff] case mismatch in snippet view article find links to article

"Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors". Physical Review Letters. 83 (24): 5162–5165. arXiv:quant-ph/9807070

Neutral atom quantum computer (3,631 words) [view diff] exact match in snippet view article find links to article

{\displaystyle |11\rangle } state. In this basis, the dressed eigenvalues and eigenvectors of the hamiltonian are given by: E L S ( 2 ) = 1 2 ( Δ ± 2 Ω

List of women in mathematics (22,953 words) [view diff] exact match in snippet view article find links to article

(1920–2012), Russian inventor of the QR algorithm for computing eigenvalues and eigenvectors Daniela Kühn (born 1973), German-English combinatorialist, expert

Glossary of areas of mathematics (7,685 words) [view diff] exact match in snippet view article find links to article

Spectral theory part of operator theory extending the concepts of eigenvalues and eigenvectors from linear algebra and matrix theory. Spectral theory of ordinary