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Schur product theoremLie algebra representationCartesian productLeibniz formula for determinantsMatrix determinant lemmaSum of two squares theoremHurewicz theoremSpecial linear lie algebraGram matrixSylvester equationProduct ruleDirichlet's approximation theoremEuler's formulaSylvester's formulaDe moivre's formulaPentagonal number theoremPythagorean trigonometric identityLie algebraAbel's identityConvolution theoremKronecker productCross productCommutation matrixTriangle inequalitySelberg trace formulaTychonoff's theoremFrobenius inner productLagrange inversion theoremMatrix decompositionTraceLie's third theoremQuadratic reciprocityTensor productMatrixHadamard's inequalityLefschetz fixed-point theoremSchur decompositionClosed-subgroup theoremHilbert transformIsomorphism theoremsPythagorean additionPlancherel theoremBounded inverse theoremPolar decompositionBessel's inequalityDarboux's theoremLiouville field theoryTensor algebraCartan decompositionSchmidt decompositionHadamard matrixMatrix multiplicationLie bracket of vector fieldsPolynomial remainder theoremJacobi identitySimons' formulaHessian matrixLevi decompositionKhintchine inequalityBrahmagupta's identityRank factorizationTriple product ruleSteinitz exchange lemmaChain ruleLu decompositionGeneral leibniz ruleKilling formPappus's centroid theoremBrun's theoremConjugate transposeDistributive propertyHermitian adjointTransfer matrixMatrix exponentialStructure constantsPythagorean theoremLax pairPolarization identityHodge star operatorIndefinite orthogonal groupKaramata's inequalityChen's theoremInvariants of tensorsSymmetric bilinear formCramer's ruleLogarithm of a matrixTensor product of representationsLaplace expansionCholesky decompositionLegendre transformationMatrix sign functionSylvester matrixCauchy's integral theoremQuadratic formImplicit function theoremAdjunction formulaAlgebra over a fieldCharacteristic polynomialStieltjes transformationGeneralized stokes theorem