Chapter 1 Vector Space
1.1 Introduction
1.2 Vector space
1.3 Subspace
1.4 Linear combinations and simultaneous linear equations
1.5 Primary Dependence and Primary Independence
1.6 Basis and Dimension
1.7 Linearly independent maximal subsets*

Chapter 2 Linear Transformations and Matrices
2.1 Linear transformation, null space, and phase space
2.2 Matrix representation of linear transformations
2.3 Composition of linear transformations and matrix multiplication
2.4 Reversibility and Isomorphism
2.5 Coordinate transformation matrix
2.6 Dual space*
2.7 Homogeneous linear differential equations with constant coefficients*

Chapter 3: Basic Matrix Operations and Systems of Linear Equations
3.1 Basic matrix operations and basic matrices
3.2 Rank and inverse of a matrix
3.3 Systems of Linear Equations: Theoretical Aspects
3.4 Systems of Linear Equations: Computational Aspects

Chapter 4 Determinant
4.1 Determinant of a quadratic square matrix
4.2 Determinant of an nth-order square matrix
4.3 Properties of determinants
4.4 Summary of key points of determinants
4.5 Strict definition of determinant*

Chapter 5 Diagonalization
5.1 Eigenvalues ​​and Eigenvectors
5.2 Diagonalizability
5.3 Matrix Limits and Markov Chains*
5.4 Invariant Subspaces and the Cayley-Hamilton Theorem

Chapter 6 Inner Space
6.1 Inner product and norm
6.2 Gram-Schmidt Orthogonalization and Orthogonal Complement
6.3 Companion operators of linear operators
6.4 Regular operators and self-complementary operators
6.5 Operators and Matrices: Unitary and Orthogonal Operators
6.6 Orthographic projection and spectral theorem
6.7 Singular value decomposition and pseudoinverse*
6.8 Bilinear and Quadratic Forms*
6.9 Einstein's special theory of relativity*
6.10 Conditioning and Rayleigh Quotients*
6.11 Orthogonal Operators and Geometry*

Chapter 7 Standard Type
7.1 Jordan Standard I: Theoretical Aspects
7.2 Jordan Standard II: Computational Aspects
7.3 Minimal polynomial
7.4 Glass Standard*

supplement
Set A
B function
C body
D complex number
E polynomial
List of F symbols

It is considered one of the most representative books in linear algebra.
Linear algebra of Friedberg, Insel, and Spence
First publication of the translated work

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Differences between the 4th and 5th editions
- The standard form (Chapter 7, Canonical Forms) that was missing from the 4th edition (International Edition) has been included again.
- Simplified the book's expressions and clarified parts that students may misunderstand.
- Improved the proofs of some theorems and added examples and practice problems.