Matrix algebra

Matrix algebra

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时间:2019-03-08

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1、1MatrixAlgebraandSolutionofMatrixEquations1.1INTRODUCTIONComputersarebestsuitedforrepetitivecalculationsandfororganizingdataintospecializedforms.Inthischapter,wereviewthematrixandvectornotationandtheirmanipulationsandapplications.Vectorisaone-dimensionalarrayofnumbersand/orcharactersarrangedasasin

2、glecolumn.Thenumberofrowsiscalledtheorderofthatvector.Matrixisanextensionofvectorwhenasetofnumbersand/orcharactersarearrangedinrectangularform.IfithasMrowsandNcolumn,thismatrixthenissaidtobeoforderMbyN.WhenM=N,thenwesaythissquarematrixisoforderN(orM).Itisobviousthatvectorisaspecialcaseofmatrixwhen

3、thereisonlyonecolumn.Consequently,avectorisreferredtoasacolumnmatrixasopposedtotherowmatrixwhichhasonlyonerow.Bracesareconventionallyusedtoindicateavectorsuchas{V}andbracketsareforamatrixsuchas[M].Inwritingacomputerprogram,DIMENSIONorDIMstatementsarenecessarytodeclarethatacertainvariableisavectoro

4、ramatrix.Suchstatementsinstructthecomputertoassignmultiplememoryspacesforkeepingthevaluesofthatvectorormatrix.Whenwedealwithalargenumberofdifferententitiesinagroup,itisbettertoarrangetheseentitiesinvectorormatrixformandrefertoaparticularentitybyspecifyingwhereitislocatedinthatgroupbypointingtother

5、ow(andcolumn)number(s).Suchasinthecaseofhaving100numbersrepresentedbythevariablenamesA,B,…,orbyA(1)throughA(100),theformerrequires100differentcharactersorcombinationsofcharactersandthelattercertainlyhastheadvantageofhavingonlyonename.TheA(1)throughA(100)arrangementistoadoptavector;thesenumberscana

6、lsobearrangedinamatrixof10rowsand10columns,or20rowsandfivecolumnsdependingonthecharacteristicsofthesenumbers.Inthecasesofcollectingtheengineeringdatafromtestsof20samplesduringfivedifferentdays,thenarrangingthese100dataintoamatrixof20rowsandfivecolumnswillbebetterthanof10rowsand10columnsbecauseeachcol

7、umncontainsthedatacollectedduringaparticularday.Intheensuingsections,weshallintroducemoredefinitionsrelatedtovectorandmatrixsuchastranspose,inverse,anddeterminant,anddiscusstheirmanipula-tionssuchasaddition,subtra

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