资源描述：
《Linear Algebra (Jim Hefferon).pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、LinearAlgebraJimHefferon¡¢13¡¢21¯¯¯12¯¯¯¯31¯¡¢1x1¢3¡¢21¯¯¯x¢12¯¯¯¯x¢31¯¡¢68¡¢21¯¯¯62¯¯¯¯81¯NotationRrealnumbersNnaturalnumbers:f0;1;2;:::g¯Ccomplexnumbersf:::¯:::gsetof...suchthat...h:::isequence;likeasetbutordermattersV;W;Uvectorspaces~v;~wvectors~0,~0Vzerovector,zerov
2、ectorofVB;DbasesE=h~e;:::;~eistandardbasisforRnn1n¯;~~±basisvectorsRepB(~v)matrixrepresentingthevectorPnsetofn-thdegreepolynomialsMn£msetofn£mmatrices[S]spanofthesetSM©NdirectsumofsubspacesV»=Wisomorphicspacesh;ghomomorphisms,linearmapsH;Gmatricest;stransformations;maps
3、fromaspacetoitselfT;SsquarematricesRepB;D(h)matrixrepresentingthemaphhi;jmatrixentryfromrowi,columnjjTjdeterminantofthematrixTR(h);N(h)rangespaceandnullspaceofthemaphR1(h);N1(h)generalizedrangespaceandnullspaceLowercaseGreekalphabetnamecharacternamecharacternamecharacte
4、ralpha®iota¶rho½beta¯kappa·sigma¾gamma°lambda¸tau¿delta±mu¹upsilonÀepsilon²nuºphiÁzeta³xi»chiÂeta´omicronopsiÃthetaµpi¼omega!Cover.ThisisCramer’sRuleforthesystemx+2y=6,3x+y=8.Thesizeofthefirstboxisthedeterminantshown(theabsolutevalueofthesizeisthearea).Thesizeofthesecond
5、boxisxtimesthat,andequalsthesizeofthefinalbox.Hence,xisthefinaldeterminantdividedbythefirstdeterminant.PrefaceInmostmathematicsprogramslinearalgebracomesinthefirstorsecondyear,followingoralongwithatleastonecourseincalculus.Whilethelocationofthiscourseisstable,latelytheconte
6、nthasbeenunderdiscussion.Someinstructorshaveexperimentedwithvaryingthetraditionaltopicsandothershavetriedcoursesfocusedonapplicationsoroncomputers.Despitethishealthydebate,mostinstructorsarestillconvinced,Ithink,thattherightcorematerialisvectorspaces,linearmaps,determin
7、ants,andeigenvaluesandeigenvectors.Applicationsandcodehaveaparttoplay,butthethemesofthecourseshouldremainunchanged.Notthatallisfinewiththetraditionalcourse.Manyofusbelievethatthestandardtexttypecoulddowithachange.Introductorytextshavetraditionallystartedwithextensivecomp
8、utationsoflinearreduction,matrixmultiplication,anddeterminants,whichtakeuphalfofthecourse.Then,whenvectorspace
