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  • Eigenvalue
    ...atrix]] <math>A</math> is a number <math>\lambda</math> that satisfies the eigenvalue equation, ...gin of this equation, the [[characteristic polynomial]] of ''A'', is the [[eigenvalue problem]], which is to find the eigenvalues and associated [[eigenvectors]]
    4 KB (731 words) - 17:16, 11 December 2008
  • Eigenvalue/Definition
    ...matrix ''A'' if '''A''' ''v'' = &lambda; ''v''; the number &lambda; is the eigenvalue of the matrix '''A''' belonging to the eigenvector ''v''.
    217 bytes (33 words) - 02:56, 2 February 2009
  • Eigenvalue/Approval
    12 bytes (1 word) - 18:20, 3 October 2007
  • Eigenvalue/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Eigenvalue]]. Needs checking by a human.
    949 bytes (118 words) - 16:12, 11 January 2010

Page text matches

  • Eigenvector
    #REDIRECT [[Eigenvalue]]
    24 bytes (2 words) - 16:47, 10 December 2008
  • Eigenvalues
    #REDIRECT [[Eigenvalue]]
    24 bytes (2 words) - 18:15, 3 October 2007
  • Rayleigh-Ritz method/Definition
    also known as linear variation method; used to solve numerically eigenvalue problems and partial differential equations with boundary conditions.
    181 bytes (22 words) - 12:13, 4 November 2008
  • Eigenvalue
    ...atrix]] <math>A</math> is a number <math>\lambda</math> that satisfies the eigenvalue equation, ...gin of this equation, the [[characteristic polynomial]] of ''A'', is the [[eigenvalue problem]], which is to find the eigenvalues and associated [[eigenvectors]]
    4 KB (731 words) - 17:16, 11 December 2008
  • Measurement in quantum mechanics
    ...of the system corresponds to some linear operator ''O'' with a number of [[eigenvalue]]s *any measurement of the property ''O'' results in an eigenvalue of ''O''
    4 KB (558 words) - 12:26, 9 May 2011
  • Eigenvalue/Definition
    ...matrix ''A'' if '''A''' ''v'' = &lambda; ''v''; the number &lambda; is the eigenvalue of the matrix '''A''' belonging to the eigenvector ''v''.
    217 bytes (33 words) - 02:56, 2 February 2009
  • Walter Ritz
    ...s formulation of the [[Rayleigh-Ritz method]] for the solution of operator eigenvalue problems and partial differential equations. Further his name is attached t
    461 bytes (60 words) - 02:47, 14 September 2013
  • Matrix inverse/Related Articles
    {{r|Eigenvalue}}
    498 bytes (63 words) - 18:22, 11 January 2010
  • Linear map/Related Articles
    {{r|Eigenvalue}}
    559 bytes (73 words) - 18:06, 11 January 2010
  • Characteristic polynomial/Related Articles
    {{r|Eigenvalue}}
    553 bytes (67 words) - 11:46, 11 January 2010
  • Hermitian operator
    Hermitian operators have real [[eigenvalue]]s. Indeed, let from which follows <math> q = q^*\, </math>, that is, the eigenvalue ''q'' is real.
    8 KB (1,273 words) - 11:29, 9 July 2009
  • Fixed point/Related Articles
    {{R|Eigenvalue}}
    818 bytes (124 words) - 03:16, 5 November 2008
  • Identity matrix/Related Articles
    {{r|Eigenvalue}}
    965 bytes (124 words) - 17:23, 11 January 2010
  • Eigenvalue/Related Articles
    Auto-populated based on [[Special:WhatLinksHere/Eigenvalue]]. Needs checking by a human.
    949 bytes (118 words) - 16:12, 11 January 2010
  • Linear algebra
    ...ems. Other topics in linear algebra, such as [[matrix|matrix algebra]], [[eigenvalue]]s and [[eigenvector]]s, [[linear operators]], [[matrix representation]]s,
    975 bytes (135 words) - 02:13, 3 September 2010
  • Electron shell
    ...squared '''S'''<sup>2</sup> with quantum number ''S'' = 0. That is, the eigenvalue of '''S'''<sup>2</sup>, which has the general form ''S''(''S'' + 1), is zer
    3 KB (430 words) - 13:54, 3 March 2023
  • Characteristic polynomial
    ...istic polynomial''' of a [[square matrix]] is a polynomial which has the [[eigenvalue]]s of the matrix as roots.
    911 bytes (131 words) - 22:35, 17 February 2009
  • Rayleigh-Ritz method
    ...thod''' is used for the computation of approximate solutions of operator [[eigenvalue]] equations and [[partial differential equation]]s. The method is based on ...sh;the time-independent [[Schrödinger equation]]&mdash;has the form of an eigenvalue equation of an operator commonly denoted by ''H'', the Hamilton (or energy)
    12 KB (1,893 words) - 04:51, 25 March 2010
  • Mixed state
    ...h>\scriptstyle \lambda_i</math> and <math>\scriptstyle \psi_i</math> is an eigenvalue and eigenvector of ''X'', respectively. For a simple illustration, consider
    5 KB (726 words) - 01:57, 30 September 2009
  • Diagonal matrix
    The diagonal entries are the [[eigenvalue]]s of a diagonal matrix.
    2 KB (230 words) - 02:39, 7 January 2009
  • Euler's theorem (rotation)
    ...nt +1. Since for such (non-identity) matrices exactly one eigenvector has eigenvalue +1, this eigenvector gives the direction of the axis. ...that the vector '''n''' is an [[eigenvector]] of the matrix '''R''' with eigenvalue &lambda; = 1.
    12 KB (1,865 words) - 02:49, 19 April 2010
  • Sturm-Liouville theory
    * Corresponding to each eigenvalue &lambda;<sub>''n''</sub> is a unique (up to a normalization constant) eigen ...neralized operator eigenvalue equation. It can be transformed to a regular eigenvalue equation by substitution of
    15 KB (2,332 words) - 04:52, 18 October 2009
  • CosFourier
    Eigenfunctions of the [[Fourier Operator]] with eigenvalue unity are also eigenfunctions of the [[CosFourier]]. Such functions can be
    2 KB (288 words) - 17:57, 8 September 2020
  • Harmonic oscillator (quantum)
    ...r these points the potential energy ''V''(''x'') is larger than the energy eigenvalue. As an example two small vertical lines are plotted: to the left of the sm ...ative, so that ''V'' &le; ''E''. This is why the region, where the energy eigenvalue of an eigenfunction is smaller than the potential energy, is called a ''cla
    10 KB (1,632 words) - 21:28, 11 September 2021
  • Legendre polynomials
    ...the differential equation has the form of an [[eigenvalue equation]] with eigenvalue &minus;''n''(''n''+1) of the operator
    7 KB (1,091 words) - 06:21, 10 September 2009
  • GF method
    ...can be done because the two equations are equivalent to the [[generalized eigenvalue problem]] ...[numerical mathematics]] several algorithms are known to solve generalized eigenvalue problems. The solution yields the matrix '''L''' and the diagonal matrix ''
    13 KB (1,996 words) - 10:52, 3 November 2021
  • Eckart conditions
    ...m, expressed in displacement coordinates, one must solve the [[generalized eigenvalue problem]] ...diagonal matrix <math>\scriptstyle \boldsymbol{\Phi}</math> contains the [[eigenvalue]]s, while
    20 KB (3,213 words) - 02:14, 23 February 2010
  • Minimal polynomial
    ...wever, the two polynomials have the same set of roots, namely the set of [[eigenvalue]]s of ''A''.
    4 KB (613 words) - 02:34, 4 January 2013
  • Fourier operator
    ...function; id set, $~S~$ is [[eigenfunction]] of the Fourier operator with eigenvalue unity. ...self-Fourier functions are [[eigenfunction]] of the Fourier operator with eigenvalue unity.
    11 KB (1,589 words) - 08:58, 9 September 2020
  • Observable (quantum computation)
    ...sharp. This means that the observable takes a value which is one of the [[Eigenvalue|eigenvalues]] of the Hermitian matrix. This set of values is the observable
    3 KB (562 words) - 00:00, 17 February 2010
  • Angular momentum (quantum)
    ...sup>2</sup> has only non-negative real eigenvalues. Therefore we write its eigenvalue as the squared number ''a''<sup>2</sup>. ...h>\scriptstyle a^2</math> and an eigenvector of ''j''<sub>''z''</sub> with eigenvalue ''b'' + 1, so that
    16 KB (2,632 words) - 04:33, 23 September 2021
  • Born-Oppenheimer approximation
    ...this molecule, is a [[partial differential equation|partial differential eigenvalue equation]] in 162 variables&mdash;the spatial coordinates of ''the electron ...'' stands for all electronic coordinates. Obviously, the electronic energy eigenvalue ''E''<sub>elec</sub> depends on the chosen positions '''R''' of the nuclei.
    20 KB (3,194 words) - 03:34, 8 November 2013
  • Molecular orbital theory
    ...s of the time-independent [[Schrödinger equation]] of molecules&mdash;the eigenvalue equation of a [[molecular Hamiltonian]] (quantum mechanical energy operato ...h is not surprising, as the corresponding HF operator equation is also an eigenvalue equation. The matrix to be diagonalized (known as the ''Fock matrix'' '''F
    20 KB (3,082 words) - 17:39, 9 December 2008
  • Trace (mathematics)
    ...''n'' roots (zeros) &lambda;<sub>''i''</sub>, ''i'' =1, ..., ''n'', the [[eigenvalue]]s of '''A''' and the following factorization holds ...s &epsilon;<sub>''i''</sub>. When ''H'' is bounded from below (its lowest eigenvalue is finite) then the sum
    12 KB (1,903 words) - 10:57, 2 February 2009
  • Schrödinger equation
    ...hat the fact that the time independent equation takes the form of a simple eigenvalue problem (thus being more amenable to mathematical analysis) that makes it s ...matically, the time-independent Schrödinger equation is an example of an [[eigenvalue problem]] whose eigenvectors &psi; are called "wavefunctions" or "quantum
    17 KB (2,678 words) - 10:12, 9 May 2011
  • Self-adjoint operator
    1. The [[eigenvalue|eigenvalues]] of a self-adjoint operator are real. As a special well-known
    4 KB (709 words) - 06:58, 23 December 2008
  • Angular momentum coupling
    ...nics]], '''angular momentum coupling''' is the procedure of constructing [[eigenvalue|eigenvectors]] of a system's [[angular momentum (quantum)|angular momentum ...em can assume a sharp (i.e., eigen-) value simultaneously with the energy (eigenvalue of the Hamiltonian) of the system.
    21 KB (3,338 words) - 10:45, 11 June 2009
  • Hydrogen-like atom
    ...ponents. It is conventional to choose ''l''<sub>''z''</sub>, which has an eigenvalue proportional to an integer usually denoted by ''m'' (the so-called [[magne The Schrödinger equation is the following eigenvalue equation of the Hamiltonian (the quantity in large square brackets):
    19 KB (2,981 words) - 18:31, 3 November 2021
  • Particle in a box
    ...ng but the [[eigenvalue problem]], and our task is to determine the energy eigenvalue(s) <math>E</math> and [[eigenstate]](s) <math>\psi</math> that solve it. To
    16 KB (2,810 words) - 11:31, 5 April 2011
  • Spherical well
    ...'spherical well problem''' is to find the [[energy]] [[eigenstates]] and [[eigenvalue|values]] of a single [[particle]] of [[mass]] <math>m</math> constrained wi
    8 KB (1,340 words) - 07:25, 27 October 2007
  • Reflection (geometry)
    ...ions have determinant &minus;1. Because &sigma; is symmetric it has real [[eigenvalue]]s; since the extension of an isometry to a complex space is unitary, its (
    8 KB (1,366 words) - 09:12, 10 August 2009
  • Rigid rotor
    The eigenvalue equation becomes The eigenvalue ''E''<sub>''j''0</sub> is (2''j'' + 1)-fold degenerate, because all eigenf
    25 KB (3,876 words) - 03:13, 1 October 2013
  • Molecular Hamiltonian
    ...lved for a sufficient number of constellations of the nuclei, the set of [[eigenvalue]]s (usually the lowest) can be seen as a [[function]] of the nuclear coor ...ignore spin and other relativistic terms and considers the solution of the eigenvalue (time-independent Schrödinger) equation of the Coulomb Hamiltonian.
    31 KB (4,757 words) - 02:20, 27 October 2013
  • Gaussian type orbitals
    ...f the [[orbital angular momentum operator]] with quantum number ''l'' = 1 [eigenvalue 1(1+1)]. ...of order ''l'', which are eigenfunctions of orbital angular momentum with eigenvalue ''l''(''l''+1). The quantum number ''l'' runs as follows
    15 KB (2,490 words) - 12:23, 19 April 2009
  • Spherical harmonics
    The eigenvalue equation can be simplified by [[separation of variables]]. We substitute into the eigenvalue equation. After dividing out &Psi; and multiplying with sin&sup2;&theta; we
    34 KB (5,282 words) - 14:21, 1 January 2011
  • DCTI
    ...he self-Fourier function is eigenfunction of the [[Fourier operator]] with eigenvalue 1;
    11 KB (1,680 words) - 18:00, 8 September 2020
  • Rotation matrix
    ...hat a rotation is characterized by a unique axis (an eigenvector with unit eigenvalue) and a unique angle. As a corollary of the theorem follows that the [[trace The eigenvalue equation can be transformed
    22 KB (3,624 words) - 01:45, 26 October 2013
  • Quantization of the electromagnetic field
    ...mentum is ℏ'''k''' [ℏ=''h''/(2π)]; the polarization &mu;=&plusmn;1 is the eigenvalue of the ''z''-component of the photon spin. ...hoton state is an eigenstate of the momentum operator, and ℏ'''k''' is the eigenvalue (the momentum of a single photon).
    23 KB (3,635 words) - 05:33, 1 April 2024
  • Symmetrizer
    ...bosons must be an eigenfunction of a transposition operator with unity as eigenvalue
    11 KB (1,655 words) - 09:52, 22 January 2009
  • Electron orbital
    ...]]-[[Fock]]-[[Roothaan]] equations, which have the form of a generalized [[eigenvalue problem]]. The dimension of this problem is equal to the number of atomic o
    10 KB (1,514 words) - 19:38, 20 November 2009
  • Fixed point
    ...ear operator]]. In this case, the fixed point is an [[eigenvector]] with [[eigenvalue]] equal to unity. For instance, the [[exponential function]] is a fixed poi
    10 KB (1,562 words) - 07:20, 13 November 2013
  • Slater determinant
    ...erminant is an eigenfunction of all three angular momentum components with eigenvalue zero, i.e., the total angular momentum quantum number of the Slater determi
    11 KB (1,582 words) - 07:52, 23 September 2009
  • Antisymmetrizer
    ...s must be an eigenfunction of a transposition operator with its parity as eigenvalue
    15 KB (2,353 words) - 17:42, 9 December 2008
  • Quantization
    ...ef> E. Schrödinger, ''Quantisierung als Eigenwerproblem'' [quantization as eigenvalue problem] Annalen der Physik, Vierte Folge, Band 79, p. 361 (1926)
    13 KB (1,900 words) - 10:49, 30 November 2009
  • Crystal field theory
    ...eigenvectors (the group theoretical functions) have been found. The first eigenvalue (energy of the state of ''T''<sub>2''g''</sub> symmetry) is 3-fold degenera
    15 KB (2,390 words) - 10:11, 5 February 2010
  • Jahn-Teller effect
    .../sub> appears linearly in the lowest first-order energy correction (lowest eigenvalue of the perturbation matrix); terms of higher order in the infinitesimal coo
    21 KB (3,426 words) - 23:58, 27 October 2013
  • Energy (science)
    ...'n''</sub> of a quantum mechanical system appear as [[eigenvalues]] of the eigenvalue equation In quantum mechanical studies the eigenvalue problem of ''any'' observable may appear occasionally. However, the observa
    43 KB (7,032 words) - 15:15, 15 August 2022
  • Archive:Monthly Write-a-Thon/October 3, 2007
    *[[User:Michael Underwood|Michael]] wrote about [[eigenvalue]]s and tidied up the laws of [[law of cosines|cosines]] and [[law of sines|
    18 KB (2,874 words) - 05:02, 8 March 2024
  • Thomas L. Saaty/Works
    *''Comparison of Eigenvalue, Logarithmic Least Squares and Least Squares Methods in Estimating Ratios,'
    20 KB (2,860 words) - 15:11, 2 October 2007
  • Quantum mechanics/Advanced
    ...le corresponds to an [[eigenvector]] of the operator, and the associated [[eigenvalue]] corresponds to the value of the observable in that eigenstate. If the ope
    37 KB (5,578 words) - 04:54, 21 March 2024
  • Tetration
    and <math>L</math> is eigenvalue of logarithm, solution of equation
    65 KB (10,203 words) - 04:16, 8 September 2014
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