Revision #197 → #1365 · back to history
addedVector spaceb7b118802e00
addedVector space axiomsce15dd1e5070
addedVectors form an abelian group5c9739a6be2e
addedLinear map6dd283f2697a
addedEquivalent linearity condition482ecd9d2d7b
addedLinear operator202ce1eb7b05
addedIsomorphism, kernel and imagef900b511b35b
addedLinear subspace873776958fea
addedImage and kernel are subspaces67939276160a
addedSpan of a seta30009a0be98
addedLinear independence9219cb8b2f8b
addedSpanning set and basis3988742d5d59
addedBasis between independent and spanning setse36e6e62bf60
addedDimension theorem for vector spacesa8bdaeb77a64
addedIsomorphic iff equal dimensionc9c6342f387f
addedFinite-dimensional vector spaceaa969629570d
addedSubspace dimension inequality61878830b67e
addedDimension of sum of subspacesf438c69d939c
addedCoordinate isomorphism from a basis52cdb0408711
addedCoordinate vector / column matrix4c5cde2fb540
addedMatrix of a linear mapef030d1028c8
addedMatrix multiplicationd2d6a40a62c4
addedSimilar matrices06a2d76ad160
addedSimilarity via row and column operations3c2d1380878d
addedSimilar to bordered identity25b26f08252b
addedSystem of linear equations2f1e0b4672cf
addedSolution as preimage under T19f2623e2fad
addedAssociated homogeneous systeme36c1f889e13
addedHomogeneous solutions are the kernel9a675933babe
addedRow operations preserve solutions524f1074a7f2
addedUnique solution when matrix invertiblec30715bd91df
addedLinear endomorphism50dc31eccd3e
addedEndomorphism as square matrixcaf05a972110
addedDeterminant55a74b1d31e5
addedInvertible iff determinant invertiblee17da7bd028e
addedCramer's rule967b49be0b14
addedDeterminant of an endomorphism4100ea352259
addedEigenvector and eigenvalue02f1dd2654ba
addedCharacteristic polynomial1f73ad234d51
addedDiagonalizablea76b402fd34f
addedSquare-free characteristic polynomial implies diagonalizable3d177efd6f38
addedSymmetric matrices are diagonalizable26be6c72c620
addedNon-diagonalizable matrix26b17e4c226b
addedFrobenius normal form613dad53ec97
addedJordan normal formf440f8a045aa
addedLinear form and dual space5e0b1041fb00
addedDual basis8d3191f8684d
addedDouble dual / bidualfe75141d3d4c
addedCanonical map to bidual is an isomorphism658e638b2890
addedDual / transpose of a linear map411905cb0696
addedMatrix of dual map is transpose6fdc2669933a
addedInner productd6873e9e7c86
addedLength of a vector5f012da2dd61
addedCauchy–Schwarz inequality3f82abb51b82
addedOrthogonality and orthonormal basis56280fab73d8
addedGram–Schmidt procedure1f37467d2d9d
addedHermitian conjugate19df2a5cc253
addedNormal operator53f48949e57f
addedCharacterization of normal matricesb7cfb80f0784
addedModule over a ringc67676f97bf5
addedFree and finitely generated modulesf196771d00db
addedSubmodule of free module over PID is free05cd93cd7754
addedEvery module is a cokernel of free modules068ada34926f
addedAlgebra (bilinear product)e67566b26ec0
addedNormed vector spacea64a78c53535
addedBanach spacecb84176ff5f4
addedHilbert space7a41d1a57063