高等应用数学问题的MATLAB求解04.ppt

Chapter4

LinearAlgebraProblemsSolvingAppliedMathematicalProblemswithMATLABCRC/TaylorFrancisPressChineseversionbyTsinghuaUniversityPressPPTbyWenbinDongandJunPeng,NortheasternUniversity,PRCProofreadbyDingyuXueYangQuanChen5/26/2025

Chapter4

LinearAlgebraProblemsInputtingSpecialMatricesFundamentalMatrixOperationsFundamentalMatrixTransformationsSolvingMatrixEquationsNonlinearFunctionsandMatrixFunctionEvaluationsChaptersummary5/26/2025

4.1InputtingSpecialMatricesNumericalmatrixinputDefiningsymbolicmatrices5/26/2025

4.1.1NumericalmatrixinputMatricesofzeros,onesandidentitymatricesMatriceswithrandomelementsDiagonalmatricesHankelmatricesHilbertmatricesandtheirinversesVandermondematricesCompanionmatrices5/26/2025

Matricesofzeros,onesand

identitymatricesThesyntaxofmatricesofzeromatrix,identitymatrixandmatrixofonessquarematrix5/26/2025

rectangularmatrixwiththesamesizeofBMulti-dimensionalarraysandotherdataformsarealsosupported5/26/2025

Example4.1GenerateazeromatrixA,andgenerateaexpandedunitmatrixBwiththesamedimensionasmatrixA.MATLABsolutions:Note:zeros()andones()canalsobeusedtodefinemulti-dimensionalarrays.5/26/2025

MatriceswithrandomelementsEachelementofmatrixsatisfiesauniformdistributionin.Thesyntax:AnuniformlydistributedrandommatrixAnrandom5/26/2025

Functionrand()canalsobeusedtodefinemulti-dimensionalrandomarraysDeclarearandommatrixofsizeTheuniformdistributionmatrixover[a,b]intervalcanbegeneratedwith5/26/2025

DefineastandardnormaldistributedN(0,1)randommatricesGeneratingN(m,s2)randomnumbers5/26/2025

DiagonalmatricesMathematicaldescriptiontoadiagonalmatrixwhereallthenon-diagonalelementsare05/26/2025

DefineamatrixfromgivenvectorExtractdiagonalvectorfromagivenmatrixDefinethe