Revision #532 → #1177 · back to history
addedEigenvector and eigenvalue (informal)d417bd4aeeb0
addedEigenvalue (corresponding factor)c0a2f64affa2
addedEigenvector of a matrix0a898addaa78
addedEquivalence of matrix and linear-transformation definitions7ce8580ec1d3
addedEigenvalue equation (eigenequation)ce06acc5ae74
addedMona Lisa shear mappingb94648eaa6a2
addedEigenfunctions of a differential operator593b735058a5
addedEigensystem, eigenspace, eigenbasisdc347363b61c
addedScalar multiples (parallel/collinear vectors)4c97269081d0
addedEigenvector and eigenvalue from matrix action8ab4973554ea
addedEquivalent form using identity matrixe3fe4f617be5
addedCharacteristic equation via determinant1aa582c83f5d
addedCharacteristic polynomiale54fb41ac438
addedFactoring the characteristic polynomial2258deabe732
addedBrief 2x2 characteristic polynomial example36a8560ecb5d
addedAlgebraic numbers entries give algebraic eigenvalues0a7719ba67c3
addedComplex conjugate eigenvalue pairsf140fe9cec43
addedSpectrum of a matrix189c31301e9c
addedSpectral radius2da640c30437
addedAlgebraic multiplicityfb7068b487d5
addedSimple and semisimple eigenvalue8d3aa9dc79c7
addedEigenspace of a matrix8f6b1cbef8f3
addedEigenspace is closed under addition and scalar multiplication62e8afe0f5c0
addedGeometric multiplicity846f11b9e70e
addedGeometric multiplicity bounded by algebraic multiplicity972f3ee99a2d
addedProof that geometric ≤ algebraic multiplicity9c5e23fedfa9
addedEigenbasis from total geometric multiplicity2c2bf355d5af
addedTrace equals sum of eigenvaluesb035890d42a4
addedDeterminant equals product of eigenvalues95583262f462
addedEigenvalues of matrix powersf2a5b31ee55e
addedInvertibility iff nonzero eigenvalues61046cfbf03d
addedHermitian matrices have real eigenvalues899e47b0f9e3
addedDefiniteness gives sign of eigenvalues133eeb37e571
addedUnitary matrix eigenvalues have absolute value one06ff04121a14
addedEigenvalues of I + A and polynomial of A0e965f7bf46e
addedRight eigenvector5d3ce849e878
addedLeft eigenvector037b9783797c
addedLeft and right eigenvectors share eigenvalues3dde34ab61d2
addedMatrix and transpose share eigenvaluesc61397839533
addedTranspose preserves geometric multiplicity720b49154c3e
addedEigendecomposition / diagonalizable matrix1bda3de6d5ae
addedDiagonalizability iff eigenvectors form a basis008e5f28db65
addedDefective matrix and Jordan normal form52f3757be9c0
addedVariational characterization of largest eigenvalue0da24c9f3151
addedTwo-dimensional matrix example596777f7a37a
addedThree-dimensional matrix example145464b5ba78
addedCyclic permutation matrix with complex eigenvalues965ae819186f
addedDiagonal matrix example65e3b5a11aaf
addedTriangular matrix exampleb6d60b1a7e31
addedMatrix with repeated eigenvalues example58b7343e26ae
addedEigenvector-eigenvalue identity86c4a121a7a7
addedEigenfunctions of a differential operator1d1be289874e
addedDerivative operator examplee211833224d2
addedGeneral eigenvalue and eigenvector2a3ff7ad65cc
addedEigenspace (general)0d09f7d8594c
addedEigenline50d33cb7cd04
addedGeometric multiplicity (general)481dd30ed58c
addedEigenspaces form a direct sum1966456f72bb
addedEigenvector-spanned subspaces are invariantf7751f513779
addedSpectrum of an operator5f12e12940ae
addedWeights in representation theory86c36c8e6915
addedHecke eigensheafbb4adf02ac90
addedDifference equation via characteristic equation454459e6045d
addedAbel–Ruffini limits explicit eigenvalue formulas1ea850c3750b
addedFinding eigenvectors by solving a linear systema5f3ceef1da4
addedPower iteration for eigenvectors3822148b4c89
addedRayleigh quotient eigenvalue estimateffe2a2fd36bd
addedRotation has complex eigenvaluesc5aea7f1fbfa
addedSqueeze mapping has reciprocal eigenvalues7cdfe54c4243
addedPrincipal component analysis9b5145835198
addedEigenvalue of a graph753d3fc46621
addedPrincipal eigenvector of a graph39fa1cc12d2d
addedPerron–Frobenius theorem for Markov chains20018863387a
addedUndamped vibration eigenvalue problem9b56cfc19f7b
addedPrincipal axes from inertia tensor8a2d99a11ca3
addedStress tensor principal components3731cd693117
addedTime-independent Schrödinger equationba92f2e44428
addedEigenchannels of transmission operator5dc48fc1bc0f
addedAtomic/molecular orbitals via Fock operator9094657d7732
addedOrientation tensor in geology0ef6d6f79002
addedBasic reproduction numberc8bde9bd717f
addedEigenfacesd07c3535d94e