PREFACE
1MATRICESANDSYSTEMSOFEQUATIONS
1SystemsofLinearEquations
2RowEchelonForm
3MatrixAlgebra
4ElementaryMatrices
SPartitionedMatrices
MATLABExercises
ChapterTestA
ChapterTestB
2DETERMINANTS
1TheDeterminantofaMatrix
2PropertiesofDeterminants
3CramersRule
MATLABExercises
ChapterTestA
ChapterTestB
3VECTORSPACES
1DefinitionandExamples
2Subspaces
3IinearIndependence
4BasisandDimension
5ChangeofBasis
6RowSpaceandColumnSpace
MATLABExercises
ChapterTestA
ChapterTestB
4LINEARTRANSFORMATIONS
1DefinitionandExamples
2MatrixRepresentationsofLinearTransformations
3Similarity
MATLABExercises
ChapterTestA
ChapterTestB
5ORTHOGONALIT
1TheScalarProductinRn
2OrthogonalSubspaces
3LeastSquaresProblems
4InnerProductSpaces
5OrthonormalSets
6TheGramSchmidt0rthogonalizationProcess
7OrthogonalPolynomials
MATLABExercises
ChapterTestA
ChapterTestB
6EIGENVALUES
1EigenvaluesandEigenvectors
2SystemsofLinearDifferentialEquations
3Diagonalization
4HermitianMatrices
5TheSingularValueDecomposition
6QuadraticForms
7PositiveDefiniteMatrices
8NonnegativeMatrices
MATLABExercises
ChapterTestA
ChapterTestB
7NUMERICALLINEARALGEBRA
1FloatingPointNumbers
2GaussianElimination
3PivotingStrategies
4MatrixNormsandConditionNumbers
5OrthogonalTransformations
6TheEigenvalueProblem
7LeastSquaresProblems
MATLABExercises
ChapterTestA
ChapterTestB
8ITERATIVEMETHODS
9CANONICALFORMS
APPENDIX:MATLAB
BIBLIOGRAPHY
ANSWERSTOSELECTEDEXERCISES
INDEX