상세정보

Preface
Chapter 1: Linear Equations. Introduction
Gaussian Elimination and Matrices
Gauss?Jordan Method
Two-Point Boundary Value Problems
Making Gaussian Elimination Work
Ill-Conditioned Systems
Chapter 2: Rectangular Systems and Echelon Forms. Row Echelon Form and Rank
The Reduced Row Echelon Form
Consistency of Linear Systems
Homogeneous Systems
Nonhomogeneous Systems
Electrical Circuits
Chapter 3: Matrix Algebra. From Ancient China to Arthur Cayley
Addition, Scalar Multiplication, and Transposition
Linearity
Why Do It This Way?
Matrix Multiplication
Properties of Matrix Multiplication 
Matrix Inversion
Inverses of Sums and Sensitivity
Elementary Matrices and Equivalence
The LU Factorization
Chapter 4: Vector Spaces. Spaces and Subspaces
Four Fundamental Subspaces
Linear Independence
Basis and Dimension
More About Rank
Classical Least Squares
Linear Transformations
Change of Basis and Similarity
Invariant Subspaces
Chapter 5: Norms, Inner Products, and Orthogonality. Vector Norms
Matrix Norms
Inner Product Spaces
Orthogonal Vectors
Gram?Schmidt Procedure
Unitary and Orthogonal Matrices
Orthogonal Reduction
The Discrete Fourier Transform
Complementary Subspaces
Range-Nullspace Decomposition
Orthogonal Decomposition
Singular Value Decomposition
Orthogonal Projection
Why Least Squares?
Angles Between Subspaces
Chapter 6: Determinants. Determinants
Additional Properties of Determinants
Chapter 7: Eigenvalues and Eigenvectors. Elementary Properties of Eigensystems
Diagonalization by Similarity Transformations
Functions of Diagonalizable Matrices
Systems of Differential Equations
Normal Matrices
Positive Definite Matrices
Nilpotent Matrices and Jordan Structure
The Jordan Form
Functions of Nondiagonalizable Matrices
Difference Equations, Limits, and Summability
Minimum Polynomials and Krylov Methods
Chapter 8: Perron-Frobenius Theory of Nonnegative Matrices. Introduction
Positive Matrices
Nonnegative Matrices
Stochastic Matrices and Markov Chains
Index.

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