LinearAlgebra FunctionSummary(Continued) CategoryFunctionDescription Eigenvaluesand singularvalues > eig Eigenvaluesandeigenvectors > svd Singularvalue decomposition > eigs Afeweigenvalues > svds Afewsingularvalues > poly Characteristic polynomial > polyeig Polynomialeigenvalue problem > condeig Conditionnumberfor eigenvalues > hess Hessenbergform > qz QZfactorization > schur Schurdecomposition Matrixfunctions > expm Matrixexponential > logm Matrixlogarithm > sqrtm Matrixsquareroot > funm Evaluategeneral matrixfunction >

SystemsofLinearEquations x=p+Z*q foranarbitraryvector > q satisfies > R*x=b . >

If > A isasquarematrixand > p isapositiveinteger,then > A^p effectivelymultiplies > A byitself > p-1 times.Forexample, > A=[111;123;136]A=111123136X=A^2 X=3610 61425102546 If > A issquareandnonsingular,then > A^(-p) effectivelymultiplies > inv(A) byitself > p-1 times: > Y=A^(-3)Y=145.0000-207.000081.0000

FunctionSummary FunctionDescription > sprandsym Sparserandomsymmetricmatrix > spdiags Sparsematrixformedfromdiagonals > FunctionDescription > sparse Createsparsematrix > full Convertsparsematrixtofullmatrix > find Findindicesofnonzeroelements > spconvert Importfromsparsematrixexternalformat > FunctionDescription > nnz Numberofnonzeromatrixelements > nonzeros Nonzeromatrixelements > nzmax Amountofstorageallocatedfornonzeromatrixelements > spones Replacenonzerosparsematrixelementswithones > spalloc Allocatespaceforsparsematrix > issparse Trueforsparsematrix > spfun Applyfunctiontononzeromatrixelements...

ThefollowingtableliststheMATLAB > optimizationfunctions. FunctionDescription > fminbnd Minimizeafunctionofonevariableonafixedinterval > fminsearch Minimizeafunctionofseveralvariables > fzero Findzeroofafunctionofonevariable > lsqnonneg Linearleastsquareswithnonnegativityconstraints > optimget Getoptimizationoptionsstructureparametervalues > optimset Createoreditoptimizationoptionsparameterstructure Formoreoptimizationcapabilities,seethe OptimizationToolboxΙUsersGuide . >