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Linear mapQuantum operationEigendecomposition of a matrixSpectrumOperator algebraRaising and lowering indicesLie algebraEigenfunctionContinuous linear operatorLie algebra representationTensor operatorOperatorLinear relationQr algorithmMatrix splittingMatrix decompositionHilbert transformHermitian adjointCoordinate vectorTranspose of a linear mapProjectionMultilinear mapCommutation matrixLogarithm of a matrixQuantum phase estimation algorithmLaplace operatorLie algebra extensionBilinear mapDirac operatorScalar multiplicationOperator theoryMatrix multiplicationTensor contractionAugmented matrixTensor decompositionNumerical linear algebraLu decompositionDifferential operatorBiconjugate gradient methodOrdered exponentialAdjoint representationLie bracket of vector fieldsStep functionAlgebraic operationConjugate gradient methodLinear differential equationRotation matrixMultilinear formTensor product of modulesMatroidResolvent formalismLogarithmic normAlgebra over a fieldEigenvalue perturbationJacobi eigenvalue algorithmLinear approximationLevinson recursionLinear algebraic groupBlock lu decompositionOrthogonal diagonalizationEigenvalues and eigenvectorsGraph fourier transformLax pairTransposeMatrix differential equationTensor reshapingCoefficient matrixSchmidt decompositionShift operatorLinear formMatrix pencilPolarization identityConvex conjugateMultiplication of vectorsExact diagonalizationAlgebraic expressionDerivationRank factorizationRepresentation theoryOrthogonalizationLogarithmic differentiationStructure constantsSchur decompositionTraceInvariant theoryCharacteristic polynomialEnergy operatorMatrix analysisGenerating function transformationLinear functionRepresentation of a lie groupPovmLogarithmic sobolev inequalitiesCartan decompositionConnectorSpectral theorySpectral theoremLinear combinationDivergenceHamiltonian vector field