【Linear Algebra Done Right】2nd Ed (1997) [Axler].pdf

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1、LinearAlgebraDoneRight,SecondEditionSheldonAxlerSpringerContentsPrefacetotheInstructorixPrefacetotheStudentxiiiAcknowledgmentsxvChapter1VectorSpaces1ComplexNumbers..........................2De?nitionofVectorSpace......................4PropertiesofVectorSpaces.....................11Subspaces

2、...............................13SumsandDirectSums........................14Exercises................................19Chapter2Finite-DimensionalVectorSpaces21SpanandLinearIndependence...................22Bases..................................27Dimension...............................31Exe

3、rcises................................35Chapter3LinearMaps37De?nitionsandExamples......................38NullSpacesandRanges.......................41TheMatrixofaLinearMap.....................48Invertibility..............................53Exercises................................59vviContent

4、sChapter4Polynomials63Degree.................................64ComplexCoef?cients........................67RealCoef?cients...........................69Exercises................................73Chapter5EigenvaluesandEigenvectors75InvariantSubspaces.........................76PolynomialsAppli

5、edtoOperators.................80Upper-TriangularMatrices.....................81DiagonalMatrices...........................87InvariantSubspacesonRealVectorSpaces...........91Exercises................................94Chapter6Inner-ProductSpaces97InnerProducts.............................98No

6、rms.................................102OrthonormalBases..........................106OrthogonalProjectionsandMinimizationProblems......111LinearFunctionalsandAdjoints..................117Exercises................................122Chapter7OperatorsonInner-ProductSpaces127Self-AdjointandNorma

7、lOperators................128TheSpectralTheorem........................132NormalOperatorsonRealInner-ProductSpaces........138PositiveOperators..........................144Isometries...............................147PolarandSingular-ValueDecompositions...