资源描述：
《伍德里奇《计量经济学导论--现代观点》2》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、xd7/14/999:28PMPage744AppendixDSummaryofMatrixAlgebrahisappendixsummarizesthematrixalgebraconcepts,includingthealgebraofTprobability,neededforthestudyofmultiplelinearregressionmodelsusingmatricesinAppendixE.Noneofthismaterialisusedinthemaintext.D.1BASICDEFINITIONSDEFINITIOND.1(Matrix
2、)Amatrixisarectangulararrayofnumbers.Moreprecisely,anmnmatrixhasmrowsandncolumns.Thepositiveintegermiscalledtherowdimension,andniscalledthecolumndimension.Weuseuppercaseboldfaceletterstodenotematrices.Wecanwriteanmnmatrixgenericallyasa11a12a13...a1na21a22a23...a2n.A[aij]..am1am
3、2am3...amnththwhereaijrepresentstheelementintheirowandthejcolumn.Forexample,a25standsforthenumberinthesecondrowandthefifthcolumnofA.Aspecificexampleofa23matrixis217A450(D.1)wherea137.TheshorthandA[aij]isoftenusedtodefinematrixoperations.DEFINITIOND.2(SquareMatrix)Asquarematri
4、xhasthesamenumberofrowsandcolumns.Thedimensionofasquarematrixisitsnumberofrowsandcolumns.744xd7/14/999:28PMPage745AppendixDSummaryofMatrixAlgebraDEFINITIOND.3(Vectors)(i)A1mmatrixiscalledarowvector(ofdimensionm)andcanbewrittenasx(x1,x2,…,xm).(ii)Ann1matrixiscalledacolumnvectorandc
5、anbewrittenasy1y2.y...ynDEFINITIOND.4(DiagonalMatrix)AsquarematrixAisadiagonalmatrixwhenallofitsdiagonalelementsarezero,thatis,aij0forallij.Wecanalwayswriteadiagonalmatrixasa1100...00a220...0.A...000...annDEFINITIOND.5(IdentityandZeroMatrices)(i)Thennidentitymatrix,denotedI,
6、orsometimesIntoemphasizeitsdimension,isthediagonalmatrixwithunity(one)ineachdiagonalposition,andzeroelsewhere:100...0010...0..IIn.....000...1(ii)Themnzeromatrix,denoted0,isthemnmatrixwithzeroforallentries.Thisneednotbeasquarematrix.D.2MATRIXOPERATIONSMatrixAdditionTwomatricesAa
7、ndB,eachhavingdimensionmn,canbeaddedelementbyele-ment:AB[aijbij].Moreprecisely,a11b11a12b12...a1nb1na21b21a22b22...a2nb2n.AB...am1bm1am2bm2...amnbmn745xd7/14/999:28PMPage746AppendixDSummaryofMatrixAlgebraForexample,217104313450423073.Matricesofdifferentdi
8、mensionscann
