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1、AdvancedMultivariateStatisticswithMatricesMathematicsandItsApplicationsManagingEditor:M.HAZEWINKELCentreforMathematicsandComputerScience,Amsterdam,TheNetherlandsVolume579AdvancedMultivariateStatisticswithMatricesbyTnuKolloõUniversityofTartu,Tartu,EstoniaandDietrichvonRosenSwed
2、ishUniversityofAgriculturalSciences,Uppsala,SwedenAC.I.P.CataloguerecordforthisbookisavailablefromtheLibraryofCongress.ISBN-101-4020-3418-0(HB)SpringerDordrecht,Berlin,Heidelberg,NewYorkISBN-101-4020-3419-9(e-book)SpringerDordrecht,Berlin,Heidelberg,NewYorkISBN-13978-1-4020-34
3、18-3(HB)SpringerDordrecht,Berlin,Heidelberg,NewYorkISBN-13978-1-4020-3419-0(e-book)SpringerDordrecht,Berlin,Heidelberg,NewYorkPublishedbySpringer,P.O.Box17,3300AADordrecht,TheNetherlands.Printedonacid-freepaperAllRightsReserved©2005SpringerNopartofthisworkmaybereproduced,store
4、dinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwrittenpermissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurposeofbeingenteredandexecutedonacomputersystem,forexcl
5、usiveusebythepurchaserofthework.PrintedintheNetherlands.ToImbi,Kaarin,Ulle,Ardo¨T˜onuTatjana,Philip,Sophie,MichaelDietrichTABLEOFCONTENTSPREFACExiINTRODUCTIONxiiiCHAPTER1.BASICMATRIXTHEORYANDLINEARALGEBRA11.1.Matrixalgebra21.1.1.Operationsandnotations21.1.2.Determinant,inverse
6、71.1.3.Rank,trace81.1.4.Positivedefinitematrices121.1.5.Factorizations121.1.6.Generalizedinverse151.1.7.Problems191.2.Algebraofsubspaces201.2.1.Introduction201.2.2.Latticesandalgebraofsubspaces211.2.3.Disjointness,orthogonalityandcommutativity251.2.4.Rangespaces341.2.5.Tensorsp
7、aces401.2.6.Matrixrepresentationoflinearoperatorsinvectorspaces451.2.7.Columnvectorspaces481.2.8.Eigenvaluesandeigenvectors511.2.9.Eigenstructureofnormalmatrices571.2.10.Eigenvalue-basedfactorizations641.2.11.Problems711.3.Partitionedmatrices721.3.1.Basicnotationandrelations72
8、1.3.2.Thecommutationmatrix791.3.3.Directproduct801.3.4.vec-op
