Chapter 1. Linear Equations
1.1. Fields
1.2. Systems of Linear Equations
1.3. Matrices and Elementary Row Operations
1.4. Row-Reduced Echelon Matrices
1.5. Matrix Multiplication
1.6. Invertible Matrices
Chapter 2. Vector Spaces
2.1. Vector Spaces
2.2. Subspaces
2.3. Bases and Dimension
2.4. Coordinates
2.5. Summary of Row-Equivalence
2.6. Computations Concerning Subspaces
Chapter 3. Linear Transformations
3.1. Linear Transformations
3.2. The Algebra of Linear Transformations
3.3. Isomorphism
3.4. Representation of Transformations by Matrices
3.5. Linear Functionals
3.6. The Double Dual
3.7. The Transpose of a Linear Transformation
Chapter 4. Polynomials
4.1. Algebras
4.2. The Algebra of Polynomials
4.3. Lagrange Interpolation
4.4. Polynomial Ideals
4.5. The Prime Factorization of a Polynomial
Chapter 5. Determinants
5.1. Commutative Rings
5.2. Determinant Functions
5.3. Permutations and the Uniqueness of Determinants
5.4. Additional Properties of Determinants
5.5. Modules
5.6. Multilinear Functions
5.7. The Grassman Ring
Chapter 6. Elementary Canonical Forms
6.1. Introduction
6.2. Characteristic Values
6.3. .Annihilating Polynomials
6.4. Invariant Subspaces
6.5. simultaneous Triangulation; Simultaneous Diagonalization
6.6. Direct-Sum Decompositions
6.7. Invarlant Direct Sums
6.8. The Primary Decomposition Theorem
Chapter 7. The Rational and Jordan Forms
7.1. Cyclic Subspaces and Annihilators
7.2. Cyclic Decompositions and the Rational Form
7.3. The Jordan Form
7.4. Computation of Invarlant Factors
7.5. Summary; Semi-Simple Operators
Chapter 8. Inner Product Spaces
8.1. Inner Products
8.2. Inner Product Spaces
8.3. Linear Functional] and Adjoints
8.4. Unitary Operators
8.5. Normal Operators
Chapter 9. Operators on Inner Product Spaces
9.1. Introduction
9.2. Forms on Inner Product Spaces
9.3. Positive Forms
9.4. More on Forms
9.5. Spectral Theory
9.6. Further Properties of Normal Operators
Chapter 10. Bilinear Forms
10.1. Bilinear Forms
10.2. Symmetric Bilinear Forms
10.3. Skew-SymmetricBilinear Forms
10.4 Groups Preserving Bilinear Forms
Appendix
A.1. Sets
A.2. Functions
A.3. Equivalence Relations
A.4. Quotient Spaces
A.5. Equivalence Relations in Linear Algebra
A.6. The Axiom of Choice
Bibliography
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1 有用 宿命论 2012-10-02 13:15:32
今儿个天不错,就先睡吧!跪著做睡著了,淚奔…MIT這版本是現下看來最適合老娘的,沒有之一~世圖V5…考慮再三,還是Minor吧…
0 有用 文喆 2014-03-21 21:45:20
数学是一门能使人保持聪明的学科。这书还不错,值得细读。我原来期望是批一些矩阵计算的书,买到以后才发现全是各种推导,和矩阵没什么关系。
1 有用 Serendipity 2014-04-20 13:04:38
觉得讲的很好但还是喜欢柯斯特立金……大概是后者总卖萌+先入为主吧
0 有用 Emma 2016-02-13 19:25:01
还行,习题有点无趣
0 有用 小寒 2024-05-03 23:16:48 重庆
很感激我们用的英文教材
0 有用 小寒 2024-05-03 23:16:48 重庆
很感激我们用的英文教材
0 有用 Emma 2016-02-13 19:25:01
还行,习题有点无趣
1 有用 Serendipity 2014-04-20 13:04:38
觉得讲的很好但还是喜欢柯斯特立金……大概是后者总卖萌+先入为主吧
0 有用 文喆 2014-03-21 21:45:20
数学是一门能使人保持聪明的学科。这书还不错,值得细读。我原来期望是批一些矩阵计算的书,买到以后才发现全是各种推导,和矩阵没什么关系。
1 有用 宿命论 2012-10-02 13:15:32
今儿个天不错,就先睡吧!跪著做睡著了,淚奔…MIT這版本是現下看來最適合老娘的,沒有之一~世圖V5…考慮再三,還是Minor吧…