Revision #526 → #1148 · back to history
addedDeterminant (informal)e4c74088ba30
addedNonzero determinant iff invertible9acf4e634e20
addedDeterminant characterized by product and triangular rules4674f4dffa49
addedAxiomatic characterization (four properties)a54828038493
addedSimilarity invariance of the determinant958790356836
addedDeterminant of a 2×2 matrixd73bd5a055e8
addedIdentity matrix has determinant 1369c60f8e887
addedTwo equal rows give determinant zero49f0307867ff
addedScaling a column scales the determinantafcc26ea5d68
added|ad−bc| is parallelogram area3d1c0142e61c
addedSigned area of parallelogram2b6811b57d5e
addedDeterminant as n-dimensional signed volumeaa85f068b1d9
addedNotation for the determinant4c533152a2c1
addedLeibniz formula for 3×3 determinant5d07413dc5c3
addedRule of Sarrusa6c8daffa14a
addedPermutation of a finite setb3fb76b47ab7
addedLeibniz formula for n×n determinant67b704070b57
addedLevi-Civita symbole4583bff01b9
addedDeterminant is multilinear in columnsa50ea6361bfe
addedDeterminant is alternatingdb3909430e11
addedUniqueness of determinant from three propertiesef5a4a8ffbb9
addedDeterminant is homogeneousb0652f76a89b
addedColumn swap multiplies determinant by −1d1bcd5492f7b
addedLinearly dependent columns give determinant 0e93b3cb943bf
addedColumn-addition leaves determinant unchanged86774108d044
addedTriangular matrix determinant equals product of diagonal31d422a7fef4
addedDeterminant via Gaussian elimination325a4ecbad7c
addedDeterminant equals determinant of transposeb83f1961c94d
addedMultiplicativity of the determinant8d9e353ba4ca
addedInvertibility iff nonzero determinant (over a field)516f57a1a7ff
addedDeterminant of an inverseca7cc0ea320d
addeddet as group homomorphism GL_n → field×d53ec1c574f1
addedCauchy–Binet formula35769f05213e
addedLaplace expansion along a rowe7fbb9b9a610
addedMinor and cofactor of a matrixe6aff5bf20a1
addedAdjugate matrix8f8104e64622
addedInverse via adjugate matrixd78c10594fe5
addedBlock-matrix determinant formuladaaefe2292bf
addedSylvester's determinant theorem4069469ff085
addedDeterminant inequality for positive semidefinite matricescab9aca640e2
addedBrunn–Minkowski concavity of nth-root determinant315b55dbd260
addedSum identity for 2×2 determinants42e1b226f63d
addedDeterminant equals product of eigenvaluesee9f81ad8fed
addedPseudo-determinant6a14c771a962
addedCharacteristic polynomialba5d6bfead71
addedSylvester's criterion for positive definitenessf6aaf9ef5d13
addeddet(exp A) = exp(tr A)09fc0c47531c
addedTrace bounds on the log determinantaad7750c5ed9
addedJacobi's formula for derivative of determinantb27aeb0df109
addedCramer's rule38f7162f2e3a
addedDeterminant detects linear dependence of columnsd14b0621067b
addedWronskian295dbae7d8ea
addedCross product as a formal 3×3 determinantc9543af48021
addedSign of determinant gives basis orientation7a2ed7260344
added|det| equals volume of parallelepiped2e1adcf477c8
addedJacobian matrix163417356030
addedChange of variables via Jacobian determinant99e20414865b
addedTriangle area via determinantacad14b42f75
addedSimilar matrices have the same determinant32cfb5b73a64
addedDeterminant of a linear endomorphismd0fab5e01133
addedDeterminant over a commutative ringe6fc054d0238
addedInvertibility over commutative rings91b8201fd1b6
addedUnimodular matrix430b02c9c8a2
addedCoordinate-free determinant via exterior power4c712bba1880
addedBerezin integral expression for the determinant41871133e672
addedPfaffian as square-root of determinant444f24620cb6
addedPermanent of a matrix17496f7ac119
addedImmanant8f57cc4cb9df
addedDeterminant for finite-dimensional algebras820098ae0093
addedFredholm determinant2cb70ae53a6b
addedFuglede−Kadison determinantb46ee3cd6b2e
addedIncompatibility over non-commutative rings83a0ced0db8e