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ID:34522350
大小:1.16 MB
页数:261页
时间:2019-03-07
《【Linear Algebra Done Right】2nd Ed (1997) [Axler].pdf》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、LinearAlgebraDoneRight,SecondEditionSheldonAxlerSpringerContentsPrefacetotheInstructorixPrefacetotheStudentxiiiAcknowledgmentsxvChapter1VectorSpaces1ComplexNumbers..........................2DefinitionofVectorSpace......................4PropertiesofVectorSpaces.....................11Subspaces
2、...............................13SumsandDirectSums........................14Exercises................................19Chapter2Finite-DimensionalVectorSpaces21SpanandLinearIndependence...................22Bases..................................27Dimension...............................31Exe
3、rcises................................35Chapter3LinearMaps37DefinitionsandExamples......................38NullSpacesandRanges.......................41TheMatrixofaLinearMap.....................48Invertibility..............................53Exercises................................59vviContent
4、sChapter4Polynomials63Degree.................................64ComplexCoefficients........................67RealCoefficients...........................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...
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