선형대수와 군

이인석

목차
머리말
개정판머리말
제1장행렬과Gauss소거법
1.1.Matrix
1.2.GaussianElimination
1.3.ElementaryMatrix
1.4.EquivalenceClass와Partition
제2장벡터공간
2.1.VectorSpace
2.2.Subspace
2.3.VectorSpace의보기
2.4.Isomorphism
제3장기저와차원
3.1.LinearCombination
3.2.일차독립과일차종속
3.3.VectorSpace의Basis
3.4.Basis의존재
3.5.VectorSpace의Dimension
3.6.우리의철학
3.7.Dimension의보기
3.8.Row-reducedEchelonForm
제4장선형사상
4.1.LinearMap
4.2.LinearMap의보기
4.3.LinearExtensionTheorem
4.4.DimensionTheorem
4.5.RankTheorem
제5장기본정리
5.1.VectorSpaceofLinearMaps
5.2.기본정리:표준기저의경우
5.3.기본정리:일반적인경우
5.4.기본정리의결과와우리의철학
5.5.ChangeofBases
5.6.SimilarityRelation
제6장행렬식
6.1.AlternatingMultilinearForm
6.2.SymmetricGroup
6.3.Determinant의정의I
6.4.Determinant의성질
6.5.Determinant의정의II
6.6.Cramer’sRule
6.7.AdjointMatrix
제7장특성다항식과대각화
7.1.Eigen-vector와Eigen-value
7.2.Diagonalization
7.3.Triangularization
7.4.Cayley-HamiltonTheorem
7.5.MinimalPolynomial
7.6.DirectSum과Eigen-space
Decomposition
제8장분해정리
8.1.Polynomial
8.2.T-InvariantSubspace
8.3.PrimaryDecompositionTheorem
8.4.Diagonalizability
8.5.T-CyclicSubspace
8.6.CyclicDecompositionTheorem
8.7.JordanCanonicalForm
제9장Rn의RigidMotion241
9.1.Rn-공간의DotProduct
9.2.Rn-공간의RigidMotion
9.3.OrthogonalOperator/Matrix
9.4.Reflection
9.5.O(2)와SO(2)
9.6.SO(3)와SO(n)
제10장내적공간
10.1.InnerProductSpace
10.2.InnerProductSpace의성질
10.3.Gram-SchmidtOrthogonalization
10.4.StandardBasis對OrthonormalBasis
10.5.InnerProductSpace의Isomorphism
10.6.OrthogonalGroup과UnitaryGroup
10.7.AdjointMatrix와그응용
제11장군
11.1.BinaryOperation과Group
11.2.Group의초보적성질
11.3.Subgroup
11.4.학부대수학의半
11.5.GroupIsomorphism
11.6.GroupHomomorphism
11.7.CyclicGroup
11.8.Group과Homomorphism의보기
11.9.LinearGroup
제12장Quotient
12.1.Coset
12.2.NormalSubgroup과QuotientGroup
12.3.QuotientSpace
12.4.IsomorphismTheorem
12.5.TriangularizationII
제13장BilinearForm
13.1.BilinearForm
13.2.QuadraticForm
13.3.OrthogonalGroup과SymplecticGroup
13.4.O(1,1)과O(3,1)
13.5.Non-degenerateBilinearForm
13.6.DualSpace와DualMap
13.7.Duality
13.8.B-Identification
13.9.TransposeOperator
제14장HermitianForm
14.1.HermitianForm
14.2.Non-degenerateHermitianForm
14.3.H-Identification과AdjointOperator
제15장SpectralTheorem
15.1.표기법과용어
15.2.NormalOperator
15.3.SymmetricOperator
15.4.OrthogonalOperator
15.5.Epilogue
제16장Topology맛보기
16.1.MatrixGroupIsomorphism
16.2.Compactness와Connectedness
참고문헌
표기법찾아보기
찾아보기

출판사서평
개정판에서는논리적으로완벽하지못한부분을보강하였고책에는없으나실제강의때언급된설명을추가하였다.특히§5.5의내용을많이보완하였고기존에독자들의요청에따라연습문제를보강하였다.행간소사다리꼴의유일성은더기초적인증명으로대체하여§3.8로옮겼다.또초판제13장의triangularization도matrixsize에관한귀납법증명으로대체하여§7.3으로옮겼고,학부2학년수준에적합하지않아서실제강의에서도생략했던초판의§15.4(“왜nondegenerate인경우만?”...
개정판에서는논리적으로완벽하지못한부분을보강하였고책에는없으나실제강의때언급된설명을추가하였다.특히§5.5의내용을많이보완하였고기존에독자들의요청에따라연습문제를보강하였다.행간소사다리꼴의유일성은더기초적인증명으로대체하여§3.8로옮겼다.또초판제13장의triangularization도matrixsize에관한귀납법증명으로대체하여§7.3으로옮겼고,학부2학년수준에적합하지않아서실제강의에서도생략했던초판의§15.4(“왜nondegenerate인경우만?”)는삭제하였다.