彼得森著的《線性代數(英文版)》內容包括大學
高年級學生為升入研究生的必備知識，如復矢量空間
，復內積，正常算子用的譜定理，雙數空間，最小多
項式，若而當典範形，有理典範形，最後一章介紹行
列式。《線性代數》與同類書相比，別具特色。例如
，高斯消元法被作為一個獲得特征值得主要工具，各
章有美妙的習題，等等。

1 Basic Theory
1.1 Induction and Well—Ordering
1.2 Elementary Linear Algebra
1.3 Fields
1.4 Vector Spaces
1.5 Bases
1.6 Linear Maps
1.7 Linear Maps as Matrices
1.8 Dimension and lsomorphism
1.9 Matrix Representations Revisited
1.10 Subspaces
1.11 Linear Maps and Subspaces
1.12 Linear Independence
1.13 Row Reduction
1.14 Dual Spaces
1.15 Quotient Spaces
2 Linear Operators
2.1 Polynomials
2.2 Linear Differential Equations
2.3 Eigenvalues
2.4 The Minimal Polynomial
2.5 Diagonalizability
2.6 Cyclic Subspaces
2.7 The Frobenius Canonical Form
2.8 The Jordan Canonical Form
2.9 The Smith Normal Form
3 Inner Product Spaces
3.1 Examples of Inner Products
3.1.1 Real Inner Products
3.1.2 Complex Inner Products
3.1.3 A Digression on Quaternions
3.2 Inner Products
3.3 Orthonormal Bases
3.4 Orthogonal Complements and Projections
3.5 Adjoint Maps
3.6 Orthogonal Projections Revisited
3.7 Matrix Exponentials
4 Linear Operators on Inner Product Spaces
4.1 Self—Adjoint Maps
4.2 Polarization and Isometries
4.3 The Spectral Theorem
4.4 Normal Operators
4.5 Unitary Equivalence
4.6 Real Forms
4.7 Orthogonal Transformations
4.8 Triangulability
4.9 The Singular Value Decomposition
4.10 The Polar Decomposition
4.11 Quadratic Forms
5 Determinants
5.1 Geometric Approach
5.2 Algebraic Approach
5.3 How to Calculate Volumes
5.4 Existence of the Volume Form
5.5 Determinants of Linear Operators
5.6 Linear Equations
5.7 The Characteristic Polynomial
5.8 Differential Equations
References
Index