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1、MatrixAlgebraFromaStatistician'sPerspectiveDavidA.HarvilleSpringerPrefaceMatrixalgebraplaysaveryimportantroleinstatisticsandinmanyotherdisci-plines.Inmanyareasofstatistics,ithasbecomeroutinetousematrixalgebrainthepresentationandthederivationorverificationofresults.Onesuchareaislinearstatistica
2、lmodels;anotherismultivariateanalysis.Intheseareas,aknowledgeofmatrixalgebraisneededinapplyingimportantconcepts,aswellasinstudyingtheunderlyingtheory,andisevenneededtousevarioussoftwarepackages(iftheyaretobeusedwithconfidenceandcompetence).Onmanyoccasions,Ihavetaughtgraduate-levelcoursesinline
3、arstatisticalmodels.Typically,theprerequisitesforsuchcoursesincludeanintroductory(un-dergraduate)courseinmatrix(orlinear)algebra.Alsotypically,thepreparationprovidedbythisprerequisitecourseisnotfullyadequate.Thereareseveralrea-sonsforthis.Thelevelofabstractionorgeneralityinthematrix(orlinear)
4、algebracoursemayhavebeensohighthatitdidnotleadtoaworkingknowledgeofthesubject,or,attheotherextreme,thecoursemayhaveemphasizedcomputationsattheexpenseoffundamentalconcepts.Further,thecontentofintroductorycoursesonmatrix(orlinear)algebravarieswidelyfrominstitutiontoinstitutionandfrominstructort
5、oinstructor.Topicssuchasquadraticforms,partitionedmatrices,andgeneralizedinversesthatplayanimportantroleinthestudyoflinearstatisticalmodelsmaybecoveredinadequatelyifatall.Anadditionaldifficultyisthatsev-eralyearsmayhaveelapsedbetweenthecompletionoftheprerequisitecourseonmatrix(orlinear)algebra
6、andthebeginningofthecourseonlinearstatisticalmodels.Thisbookisaboutmatrixalgebra.Adistinguishingfeatureisthatthecontent,theorderingoftopics,andthelevelofgeneralityareonesthatIconsiderappro-priateforsomeonewithaninterestinlinearstatisticalmodelsandperhapsalsoviforsomeonewithaninterestinanother
7、areaofstatisticsorinarelateddiscipline.Ihavetriedtokeepthepresentationatalevelthatissuitableforanyonewhohashadanintroductorycourseinmatrix(orlinear)algebra.Infact,thebookisessentiallyself-contained,anditishopedthatmuch,ifnotall,ofthematerialm
