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UniversityCollegeofSoutheastNorway
http://home.hit.no/~hansha
IntroductiontoMATLABHans-PetterHalvorsen,2016.11.01
PrefaceMATLABisatoolfortechnicalcomputing,computationandvisualizationinanintegratedenvironment.ThisdocumentexplainsthebasicconceptsinMATLAB.
MATLABisanabbreviationforMATrixLABoratory,soitiswellsuitedformatrixmanipulationandproblemsolvingrelatedtoLinearAlgebra.
MATLABofferslotsofadditionalToolboxesfordifferentareassuchasControlDesign,ImageProcessing,DigitalSignalProcessing,etc.
FormoreinformationaboutMATLAB,seemyBlog:http://home.hit.no/~hansha
iii
TableofContentsPreface......................................................................................................................................2
TableofContents.....................................................................................................................iii
1 Introduction......................................................................................................................1
1.1 Help.............................................................................................................................2
2 StartusingMATLAB...........................................................................................................4
2.1 TheMATLABEnvironment..........................................................................................4
2.1.1 CommandWindow..............................................................................................4
2.1.2 CommandHistory................................................................................................5
2.2 Variables.....................................................................................................................6
2.2.1 Workspace...........................................................................................................6
2.2.2 CurrentDirectory.................................................................................................7
2.3 Usefulcommands.......................................................................................................8
3 MatricesandVectors........................................................................................................9
3.1 Usefulcommands.....................................................................................................11
4 Scriptsandfunctions–MFiles........................................................................................12
4.1 Scripts.......................................................................................................................12
4.2 Functions..................................................................................................................13
5 FlowControl....................................................................................................................15
5.1 If-elseStatement......................................................................................................15
5.2 SwitchandCaseStatement......................................................................................15
5.3 Forloop.....................................................................................................................16
5.4 Whileloop.................................................................................................................16
iv TableofContents
6 Plotting............................................................................................................................17
7 LinearAlgebra.................................................................................................................19
7.1 Vectors......................................................................................................................19
7.2 Matrices....................................................................................................................20
7.2.1 Transpose..........................................................................................................20
7.2.2 Diagonal.............................................................................................................20
7.2.3 Triangular..........................................................................................................21
7.2.4 MatrixMultiplication.........................................................................................21
7.2.5 MatrixAddition.................................................................................................22
7.2.6 Determinant......................................................................................................22
7.2.7 InverseMatrices................................................................................................23
7.3 Eigenvalues...............................................................................................................24
7.4 SolvingLinearEquations...........................................................................................25
7.5 LUfactorization.........................................................................................................26
7.6 TheSingularValueDecomposition(SVD).................................................................27
7.7 Commands................................................................................................................27
8 Toolboxes........................................................................................................................28
9 WhatsNext?....................................................................................................................29
QuickReference......................................................................................................................31
9.1 General.....................................................................................................................31
9.2 Matrices....................................................................................................................31
9.3 LinearAlgebra...........................................................................................................31
1
1 IntroductionMATLABisatoolfortechnicalcomputing,computationandvisualizationinanintegratedenvironment,e.g.,
• Mathandcomputation• Algorithmdevelopment• Dataacquisition• Modeling,simulation,andprototyping• Dataanalysis,exploration,andvisualization• Scientificandengineeringgraphics• Applicationdevelopment,includinggraphicaluserinterfacebuilding
MATLABisdevelopedbyTheMathWorks.MATLABisashort-termforMATrixLABoratory.MATLABisinuseworld-widebyresearchersanduniversities.
Formoreinformation,seewww.mathworks.com
BelowweseetheMATLABEnvironment:
MATLABhasthefollowingwindows:
• CommandWindow
2 Introduction
Tutorial:IntroductiontoMATLAB
• CommandHistory• Workspace• CurrentDirectory
TheCommandwindowisthemainwindow.UsetheCommandWindowtoentervariablesandtorunfunctionsandM-filesscripts(moreaboutm-fileslater).
Watchthefollowing“GettingStartedwithMATLAB”video:
http://www.mathworks.com/demos/matlab/getting-started-with-matlab-video-tutorial.html
1.1 HelpMATLABhasacomprehensiveHelpsystem.
Youmayalsotypehelpinyourcommandwindow
>>help
Ormorespecific,e.g.,
>>help plot
3 Introduction
Tutorial:IntroductiontoMATLAB
IadviseyoutotestalltheexamplesinthistextinMATLABinordertogetfamiliarwiththeprogramanditssyntax.Allexamplesinthetextareoutlinedinaframelikethis:
>> …
4
2 StartusingMATLABThischapterexplainsthebasicconceptsinMATLAB.
Thetopicsareasfollows:
• TheMATLABEnvironmento CommandWindowo CommandHistoryo Workspaceo CurrentDirectory
• Variables
2.1 TheMATLABEnvironment
2.1.1 CommandWindow
TheCommandwindowisthemainwindow.UsetheCommandWindowtoentervariablesandtorunfunctionsandM-filesscripts(moreaboutm-fileslater).
YoutypeallyourcommandsafterthecommandPrompt“>>”,e.g.,definingthefollowingmatrix
5 StartusingMATLAB
Tutorial:IntroductiontoMATLAB
𝐴 = 1 20 3
TheMATLABsyntaxisasfollows:
>> A = [1 2;0 3]
Or
>> A = [1,2;0,3]
Ifyou,foranexample,wanttofindtheanswerto
𝑎 + 𝑏,𝑤ℎ𝑒𝑟𝑒𝑎 = 4, 𝑏 = 3
>>a=4 >>b=3 >>a+b
MATLABthenresponds:
ans = 7
2.1.2 CommandHistory
StatementsyouenterintheCommandWindowareloggedintheCommandHistory.FromtheCommandHistory,youcanviewandsearchforpreviouslyrunstatements,aswellascopyandexecuteselectedstatements.YoucanalsocreateanM-filefromselectedstatements.
6 StartusingMATLAB
Tutorial:IntroductiontoMATLAB
2.2 VariablesVariablesaredefinedwiththeassignmentoperator,“=”.MATLABisdynamicallytyped,meaningthatvariablescanbeassignedwithoutdeclaringtheirtype,andthattheirtypecanchange.Valuescancomefromconstants,fromcomputationinvolvingvaluesofothervariables,orfromtheoutputofafunction.Forexample:
>> x = 17 x = 17 >> x = 'hat' x = hat >> x = [3*4, pi/2] x = 12.0000 1.5708 >> y = 3*sin(x) y = -1.6097 3.0000
Unlikemanyotherlanguages,wherethesemicolonisusedtoterminatecommands,inMATLABthesemicolonservestosuppresstheoutputofthelinethatitconcludes.
>> a=5 a = 5 >> a=6; >>
Asyousee,whenyoutypeasemicolon(;)afterthecommand,MATLABwillnotrespond.
2.2.1 Workspace
TheWorkspacewindowlistallyourvariablesusedaslongyouhaveMATLABopened.
7 StartusingMATLAB
Tutorial:IntroductiontoMATLAB
Youcouldalsousethefollowingcommand
>>who
Thiscommandlistallthecommandsused
or
>>whos
Thiscommandlistsallthecommandwiththecurrentvalues,dimensions,etc.
Thecommandclear,willclearallthevariables.
>>clear
2.2.2 CurrentDirectory
TheCurrentDirectorywindowlistalmfiles,etc.
8 StartusingMATLAB
Tutorial:IntroductiontoMATLAB
2.3 UsefulcommandsHerearesomeusefulcommands:
Command Description
help Help
help x Givesyouhelponsubject“x”
who, whos Getlistofvariables
clear ClearsallvariablesintheWorkspace
clear x Clearsthevariablex
what ListallmfilesintheWorkingFolder
9
3 MatricesandVectorsThischapterexplainsthebasicconceptsofusingvectorsandmatricesinMATLAB.
Topics:
• MatricesandVectorssyntax• Matricesfunctions
MATLABisa"MatrixLaboratory",andassuchitprovidesmanyconvenientwaysforcreatingvectors,matrices,andmulti-dimensionalarrays.IntheMATLAB,avectorreferstoaonedimensional(1×NorN×1)matrix,commonlyreferredtoasanarrayinotherprogramminglanguages.Amatrixgenerallyreferstoa2-dimensionalarray,i.e.anm×narraywheremandnaregreaterthanorequalto1.Arrayswithmorethantwodimensionsarereferredtoasmultidimensionalarrays.
MATLABprovidesasimplewaytodefinesimplearraysusingthesyntax:“init:increment:terminator”.Forinstance:
>> array = 1:2:9 array = 1 3 5 7 9
definesavariablenamedarray(orassignsanewvaluetoanexistingvariablewiththenamearray)whichisanarrayconsistingofthevalues1,3,5,7,and9.Thatis,thearraystartsat1(theinitvalue),incrementswitheachstepfromthepreviousvalueby2(theincrementvalue),andstopsonceitreaches(ortoavoidexceeding)9(theterminatorvalue).
Theincrementvaluecanactuallybeleftoutofthissyntax(alongwithoneofthecolons),touseadefaultvalueof1.
>> ari = 1:5 ari = 1 2 3 4 5
assignstothevariablenamedarianarraywiththevalues1,2,3,4,and5,sincethedefaultvalueof1isusedastheincrementer.
Notethattheindexingisone-based,whichistheusualconventionformatricesinmathematics.Thisisatypicalforprogramminglanguages,whosearraysmoreoftenstartwithzero.
10 MatricesandVectors
Tutorial:IntroductiontoMATLAB
Matricescanbedefinedbyseparatingtheelementsofarowwithblankspaceorcommaandusingasemicolontoterminateeachrow.Thelistofelementsshouldbesurroundedbysquarebrackets:[].Parentheses:()areusedtoaccesselementsandsubarrays(theyarealsousedtodenoteafunctionargumentlist).
>> A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> A(2,3) ans = 11
Setsofindicescanbespecifiedbyexpressionssuchas"2:4",whichevaluatesto[2,3,4].Forexample,asubmatrixtakenfromrows2through4andcolumns3through4canbewrittenas:
>> A(2:4,3:4) ans = 11 8 7 12 14 1
Asquareidentitymatrixofsizencanbegeneratedusingthefunctioneye,andmatricesofanysizewithzerosoronescanbegeneratedwiththefunctionszerosandones,respectively.
>> eye(3) ans = 1 0 0 0 1 0 0 0 1 >> zeros(2,3) ans = 0 0 0 0 0 0 >> ones(2,3) ans = 1 1 1 1 1 1
MostMATLABfunctionscanacceptmatricesandwillapplythemselvestoeachelement.Forexample,mod(2*J,n)willmultiplyeveryelementin"J"by2,andthenreduceeachelementmodulo"n".MATLABdoesincludestandard"for"and"while"loops,butusingMATLAB'svectorizednotationoftenproducescodethatiseasiertoreadandfastertoexecute.Thiscode,excerptedfromthefunctionmagic.m,createsamagicsquareMforoddvaluesofn
11 MatricesandVectors
Tutorial:IntroductiontoMATLAB
(thebuilt-inMATLABfunctionmeshgridisusedheretogeneratesquarematricesIandJcontaining1:n).
[J,I] = meshgrid(1:n); A = mod(I+J-(n+3)/2,n); B = mod(I+2*J-2,n); M = n*A + B + 1;
3.1 UsefulcommandsHerearesomeusefulcommands:
Command Description
eye(x), eye(x,y) Identitymatrixoforderx
ones(x), ones(x,y) Amatrixwithonlyones
zeros(x), zeros(x,y) Amatrixwithonlyzeros
diag([x y z]) Diagonalmatrix
size(A) DimensionofmatrixA
A’ InverseofmatrixA
12
4 Scriptsandfunctions–MFiles
M-filesaretextfilescontainingMATLABcode.UsetheMATLABEditororanothertexteditortocreateafilecontainingthesamestatementsyouwouldtypeattheMATLABcommandline.Savethefileunderanamethatendsin“.m”.
4.1 ScriptsCreateanewm-filefromtheFile→NewmenuortheNewbuttonontheToolbar.
Thebuilt-inEditorforcreatingandmodifyingm-files:
13 Scriptsandfunctions–MFiles
Tutorial:IntroductiontoMATLAB
Runningam-fileintheCommandwindow:
4.2 FunctionsYoumaycreateyourownfunctionsandsavethemasam-file.
Example:
Createafunctioncalled“linsolution”whichsolve 𝐴𝑥 = 𝑏 → 𝑥 = 𝐴34𝑏
Belowweseehowthem-fileforthisfunctionlookslike:
14 Scriptsandfunctions–MFiles
Tutorial:IntroductiontoMATLAB
YoumaydefineAandbintheCommandwindowandtheusethefunctiononordertofindx:
>> A=[1 2;3 4]; >> b=[5;6]; >> x = linsolution(A,b) x = -4.0000 4.5000
Afterthefunctiondeclaration(function [x] = linsolution(A,b))inthem.file,youmaywriteadescriptionofthefunction.ThisisdonewiththeCommentsign“%”beforeeachline.
FromtheCommandwindowyoucanthentype“help <function name>”inordertoreadthisinformation:
>> help linsolution Solves the problem Ax=b using x=inv(A)*b Created By Hans-Petter Halvorsen
15
5 FlowControlThischapterexplainsthebasicconceptsofflowcontrolinMATLAB.
Thetopicsareasfollows:
• If-elsestatement• Switchandcasestatement• Forloop• Whileloop
5.1 If-elseStatementTheifstatementevaluatesalogicalexpressionandexecutesagroupofstatementswhentheexpressionistrue.Theoptionalelseifandelsekeywordsprovidefortheexecutionofalternategroupsofstatements.Anendkeyword,whichmatchestheif,terminatesthelastgroupofstatements.Thegroupsofstatementsaredelineatedbythefourkeywords—nobracesorbracketsareinvolved.
Example:
n=5 if n > 2 M = eye(n) elseif n < 2 M = zeros(n) else M = ones(n) end
5.2 SwitchandCaseStatementTheswitchstatementexecutesgroupsofstatementsbasedonthevalueofavariableorexpression.Thekeywordscaseandotherwisedelineatethegroups.Onlythefirstmatchingcaseisexecuted.Theremustalwaysbeanendtomatchtheswitch.
Example:
n=2 switch(n)
16 FlowControl
Tutorial:IntroductiontoMATLAB
case 1 M = eye(n) case 2 M = zeros(n) case 3 M = ones(n) end
5.3 ForloopTheforlooprepeatsagroupofstatementsafixed,predeterminednumberoftimes.Amatchingenddelineatesthestatements.
Example:
m=5 for n = 1:m r(n) = rank(magic(n)); end r
5.4 WhileloopThewhilelooprepeatsagroupofstatementsanindefinitenumberoftimesundercontrolofalogicalcondition.Amatchingenddelineatesthestatements.
Example:
m=5; while m > 1 m = m - 1; zeros(m) end
17
6 PlottingThischapterexplainsthebasicconceptsofcreatingplotsinMATLAB.
Topics:
• BasicPlotcommands
Functionplotcanbeusedtoproduceagraphfromtwovectorsxandy.Thecode:
x = 0:pi/100:2*pi; y = sin(x); plot(x,y)
producesthefollowingfigureofthesinefunction:
Three-dimensionalgraphicscanbeproducedusingthefunctionssurf,plot3ormesh.
[X,Y] = meshgrid(-10:0.25:10,-10:0.25:10); f = sinc(sqrt((X/pi).^2+(Y/pi).^2)); mesh(X,Y,f); axis([-10 10 -10 10 -0.3 1]) xlabel('{\bfx}') ylabel('{\bfy}') zlabel('{\bfsinc} ({\bfR})') hidden off
18 Plotting
Tutorial:IntroductiontoMATLAB
Thiscodeproducesthefollowing3Dplot:
19
7 LinearAlgebraLinearalgebraisabranchofmathematicsconcernedwiththestudyofmatrices,vectors,vectorspaces(alsocalledlinearspaces),linearmaps(alsocalledlineartransformations),andsystemsoflinearequations.
MATLABarewellsuitedforLinearAlgebra.
7.1 VectorsGivenavectorx
𝑥 =
𝑥4𝑥5⋮𝑥7
∈ 𝑅7
Example:
𝑥 =123
>> x=[1; 2; 3] x = 1 2 3
TheTransposeofvectorx:
𝑥: = 𝑥4 𝑥5 ⋯ 𝑥7 ∈ 𝑅4<7
>> x' ans = 1 2 3
TheLengthofvectorx:
𝑥 = 𝑥:𝑥 = 𝑥45 + 𝑥55 + ⋯+ 𝑥75
Orthogonality:
20 LinearAlgebra
Tutorial:IntroductiontoMATLAB
𝑥:𝑦 = 0
7.2 MatricesGivenamatrixA:
𝐴 =𝑎44 ⋯ 𝑎4>⋮ ⋱ ⋮𝑎74 ⋯ 𝑎7>
∈ 𝑅7<>
Example:
𝐴 = 0 1−2 −3
>> A=[0 1;-2 -3] A = 0 1 -2 -3
7.2.1 Transpose
TheTransposeofmatrixA:
𝐴: =𝑎44 ⋯ 𝑎74⋮ ⋱ ⋮
𝑎4> ⋯ 𝑎7>∈ 𝑅><7
Example:
𝐴: = 0 1−2 −3
:= 0 −2
1 −3
>> A' ans = 0 -2 1 -3
7.2.2 Diagonal
TheDiagonalelementsofmatrixAisthevector
𝑑𝑖𝑎𝑔(𝐴) =
𝑎44𝑎55⋮𝑎FF
∈ 𝑅FGHIJ(<,>)
21 LinearAlgebra
Tutorial:IntroductiontoMATLAB
Example:
>> diag(A) ans = 0 -3
TheDiagonalmatrixΛisgivenby:
Λ =
𝜆4 0 ⋯ 00 𝜆5 ⋯ 0⋮ ⋮ ⋱ ⋮0 0 ⋯ 𝜆7
∈ 𝑅7<7
GiventheIdentitymatrixI:
𝐼 =
1 0 ⋯ 00 1 ⋯ 0⋮ ⋮ ⋱ ⋮0 0 ⋯ 1
∈ 𝑅7<>
Example:
>> eye(3) ans = 1 0 0 0 1 0 0 0 1
7.2.3 Triangular
LowerTriangularmatrixL:
𝐿 =. 0 0⋮ ⋱ 0. ⋯ .
UpperTriangularmatrixU:
𝑈 =. ⋯ .0 ⋱ ⋮0 0 .
7.2.4 MatrixMultiplication
Giventhematrices 𝐴 ∈ 𝑅7<> and 𝐵 ∈ 𝑅><F,then
𝐶 = 𝐴𝐵 ∈ 𝑅7<F
22 LinearAlgebra
Tutorial:IntroductiontoMATLAB
where
𝑐TU = 𝑎TV𝑏VU
7
VG4
Example:
>> A=[0 1;-2 -3] A = 0 1 -2 -3 >> B=[1 0;3 -2] B = 1 0 3 -2 >> A*B ans = 3 -2 -11 6
Note!
𝐴𝐵 ≠ 𝐵𝐴
𝐴 𝐵𝐶 = 𝐴𝐵 𝐶
𝐴 + 𝐵 𝐶 = 𝐴𝐶 + 𝐵𝐶
𝐶 𝐴 + 𝐵 = 𝐶𝐴 + 𝐶𝐵
7.2.5 MatrixAddition
Giventhematrices 𝐴 ∈ 𝑅7<> and 𝐵 ∈ 𝑅7<>,then
𝐶 = 𝐴 + 𝐵 ∈ 𝑅7<>
Example:
>> A=[0 1;-2 -3] >> B=[1 0;3 -2] >> A+B ans = 1 1 1 -5
7.2.6 Determinant
Givenamatrix 𝐴 ∈ 𝑅7<7,thentheDeterminantisgiven:
23 LinearAlgebra
Tutorial:IntroductiontoMATLAB
det 𝐴 = 𝐴
Givena2x2matrix
𝐴 =𝑎44 𝑎45𝑎54 𝑎55 ∈ 𝑅5<5
Then
det 𝐴 = 𝐴 = 𝑎44𝑎55 − 𝑎54𝑎45
Example:
A = 0 1 -2 -3 >> det(A) ans = 2
Noticethat
det 𝐴𝐵 = det 𝐴 det 𝐵
and
det 𝐴: = det(𝐴)
Example:
>> det(A*B) ans = -4 >> det(A)*det(B) ans = -4 >> det(A') ans = 2 >> det(A) ans = 2
7.2.7 InverseMatrices
24 LinearAlgebra
Tutorial:IntroductiontoMATLAB
Theinverseofaquadraticmatrix 𝐴 ∈ 𝑅7<7 isdefinedby:
𝐴34
if
𝐴𝐴34 = 𝐴34𝐴 = 𝐼
Fora2x2matrixwehave:
𝐴 =𝑎44 𝑎45𝑎54 𝑎55 ∈ 𝑅5<5
Theinverse 𝐴34 isgivenby
𝐴34 =1
det(𝐴)𝑎55 −𝑎45−𝑎54 𝑎44 ∈ 𝑅5<5
Example:
A = 0 1 -2 -3 >> inv(A) ans = -1.5000 -0.5000 1.0000 0
Noticethat:
𝐴𝐴34 = 𝐴34𝐴 = 𝐼
→ProvethisinMATLAB
7.3 EigenvaluesGiven 𝐴 ∈ 𝑅7<7,thentheEigenvaluesisdefinedas:
det 𝜆𝐼 − 𝐴 = 0
Example:
A = 0 1 -2 -3 >> eig(A) ans = -1 -2
25 LinearAlgebra
Tutorial:IntroductiontoMATLAB
7.4 SolvingLinearEquationsGiventhelinearequation
𝐴𝑥 = 𝑏
withthesolution:
𝑥 = 𝐴34𝑏
(AssumingthattheinverseofAexists)
Example:
Theequations
𝑥4 + 2𝑥5 = 53𝑥4 + 4𝑥5 = 6
maybewritten
𝐴𝑥 = 𝑏
1 23 4
𝑥4𝑥5 = 5
6
where
𝐴 = 1 23 4
𝑥 =𝑥4𝑥5
𝑏 = 56
Thesolutionis:
A = 1 2 3 4 >> b=[5;6] b = 5 6 >> x=inv(A)*b x = -4.0000 4.5000
InMATLAByoucouldalsowrite“x=A\b”,whichshouldgivethesameanswer.ThissyntaxcanalsobeusedwhentheinverseofAdon’texists.
26 LinearAlgebra
Tutorial:IntroductiontoMATLAB
Example:
>> A=[1 2;3 4;7 8] >> x=inv(A)*b ??? Error using ==> inv Matrix must be square. >> x=A\b x = -3.5000 4.1786
7.5 LUfactorizationLUfactorizationof 𝐴 ∈ 𝑅7<> isgivenby
𝐴 = 𝐿𝑈
where
Lisalowertriangularmatrix
Uisauppertriangularmatrix
TheMATLABsyntaxis[L,U]=lu(A)
Example:
>> A=[1 2;3 4] >> [L,U]=lu(A) L = 0.3333 1.0000 1.0000 0 U = 3.0000 4.0000 0 0.6667
OrsometimesLUfactorizationof 𝐴 ∈ 𝑅7<> isgivenby
𝐴 = 𝐿𝑈 = 𝐿𝐷𝑈
where
Disadiagonalmatrix
TheMATLABsyntaxis[L,U,P]=lu(A)
Example:
>> A=[1 2;3 4] A = 1 2 3 4
27 LinearAlgebra
Tutorial:IntroductiontoMATLAB
>> [L,U,P]=lu(A) L = 1.0000 0 0.3333 1.0000 U = 3.0000 4.0000 0 0.6667 P = 0 1 1 0
7.6 TheSingularValueDecomposition(SVD)TheSingularvalueDecomposition(SVD)ofthematrix 𝐴 ∈ 𝑅7<> isgivenby
𝐴 = 𝑈𝑆𝑉:
where
Uisaorthogonalmatrix
Visaorthogonalmatrix
Sisadiagonalsingularmatrix
Example:
>> A=[1 2;3 4]; >> [U,S,V] = svd(A) U = -0.4046 -0.9145 -0.9145 0.4046 S = 5.4650 0 0 0.3660 V = -0.5760 0.8174 -0.8174 -0.5760
7.7 Commands
Command Description
[L,U]=lu(A)
[L,U,P]=lu(A)LUFactorization
[U,S,V] = svd(A) SingularValueDecomposition(SVD)
28
8 ToolboxesToolboxesarespecializedcollectionsofM-filesbuiltforsolvingparticularclassesofproblems,e.g.,
• ControlSystemToolbox• SignalProcessingToolbox• StatisticsToolbox• SystemidentificationToolbox• etc.
29
9 WhatsNext?TherearelotsofusefulresourcestodigintoifyouwanttolearnmoreaboutMATLAB.
TypedemointheCommandwindowinMATLAB
>>demo
Inthe“GettingStatedwithDemos”intheMATLAHelpsystemyougetaccesstotonsofDemosinformofM-files,Videos,etc.
FormoreinformationaboutMATLAB,seewww.mathworks.com
AttheMathWorkshomepagetherearelotsofDocumentation,Examples,Videos,TipsandTricks,etc.
AnotherresourceistheMATLABdocumentation(maybedownloadedaspdffilesfromwww.mathworks.com),suchas:
• MATLABDesktopToolsandDevelopmentEnvironment• MATLABGettingStartedGuide• MATLABFunctionReference
30 LinearAlgebra
Tutorial:IntroductiontoMATLAB
• MATLABMathematics• MATLABGraphics• Etc.
31
QuickReference
9.1 General
Command Description
help Help
help x Givesyouhelponsubject“x”
who, whos Getlistofvariables
clear ClearsallvariablesintheWorkspace
clear x Clearsthevariablex
what ListallmfilesintheWorkingFolder
9.2 Matrices
Command Description
eye(x), eye(x,y) Identitymatrixoforderx
ones(x), ones(x,y) Amatrixwithonlyones
zeros(x), zeros(x,y) Amatrixwithonlyzeros
diag([x y z]) Diagonalmatrix
size(A) DimensionofmatrixA
A’ InverseofmatrixA
9.3 LinearAlgebra
Command Description
QuickReference
Tutorial:IntroductiontoMATLAB
[L,U]=lu(A)
[L,U,P]=lu(A)LUFactorization
[U,S,V] = svd(A) SingularValueDecomposition(SVD)
Hans-PetterHalvorsen,M.Sc.
E-mail:hans.p.halvorsen@hit.no
Blog:http://home.hit.no/~hansha/
UniversityCollegeofSoutheastNorway
www.usn.no
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