从英文原词解析线性代数术语-豆柴文库

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从英文原词解析线性代数术语
Linearalgebraisamathematicaldisciplinethatdealswithvectorspacesandlineartransformations.Itsconceptsareusedextensivelyinvariousfieldssuchasphysics,engineering,computerscience,andeconomics.Theterminologyusedinlinearalgebracanoftenbeconfusingtothosenewtothesubject.Inthispaper,wewilldiscusssomeofthekeytermsinlinearalgebraandprovideanexplanationoftheirmeaning.
Vector
Avectorisaquantitythathasbothmagnitudeanddirection.Inlinearalgebra,avectorisrepresentedbyalistofnumberscalledcoordinates.Thesecoordinatescanbearrangedinacolumnorrowvector.Forexample,avectorinthree-dimensionalspacecanberepresentedasacolumnvector(a,b,c)orarowvector(abc).
Scalar
Ascalarisasinglerealnumberthatisusedtoscaleavector.Scalarscanbemultipliedbyavectortoproduceanewvectorwithadifferentmagnitudebutthesamedirection.Forexample,multiplyingavector(a,b,c)withascalarkwouldresultinanewvector(ka,kb,kc).
Matrix
Amatrixisarectangulararrayofnumbersarrangedinrowsandcolumns.Matricesareusedinlinearalgebratorepresentlineartransformationsbetweenvectorspaces.Amatrixcanbemultipliedbyavector,resultinginanewvector.
Transpose
Thetransposeofamatrixisobtainedbyinterchangingitsrowsandcolumns.Thetransposeofarowvectorbecomesacolumnvector,andthetransposeofacolumnvectorbecomesarowvector.ThetransposeofamatrixisdenotedbyA^T.
Determinant
Thedeterminantofamatrixisascalarvaluethatiscomputedfromtheelementsofthematrix.Thedeterminantisusedtodetermineifamatrixisinvertible,whichmeansthatamatrixcanbeusedtosolveasystemoflinearequations.Amatrixisinvertibleifitsdeterminantisnonzero.
Inverse
Theinverseofamatrixisanewmatrixthatcanbemultipliedbytheoriginalmatrixtoproducetheidentitymatrix.Theidentitymatrixisaspecialmatrixthathasonesonthediagonalandzeroseverywhereelse.TheinverseofamatrixcanbeusedtosolveasystemoflinearequationsandisdenotedbyA^-1.
EigenvalueandEigenvector
Aneigenvalueisascalarvaluethatisassociatedwithaneigenvector.Aneigenvectorisavectorthat,whenmultipliedbyamatrix,resultsinanewvectorthatisascalarmultipleoftheoriginaleigenv