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· 제목 : Matrix Analysis and Applied Linear Algebra Book and Solutions Manual [With CDROM] (Hardcover)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 선형대수학
· ISBN : 9780898714548
· 쪽수 : 718쪽
· 출판일 : 2000-06-01
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 선형대수학
· ISBN : 9780898714548
· 쪽수 : 718쪽
· 출판일 : 2000-06-01
목차
- 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.
