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
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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 Non-diagonalizable 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.
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0 有用 尘涌酱 2020-08-10 16:41:04
简明易懂
1 有用 林同学 2020-08-04 09:21:43
这本书可以说是这个领域不可多得的好书,尤其对我这种不是数学专业的人。尤其讲特征值那一章,把矩阵函数那一套讲的很清楚,还有案例。然后观点似乎也挺高的,很多地方应该是采用了泛函分析的一些思想。总之一句话,牛逼。
2 有用 Chen_1st 2010-10-20 15:06:41
比较好的矩阵分析入门书籍。感觉基本上不需要什么特别的预备知识就能读懂。
0 有用 ×○×~~~ 2013-02-17 06:23:22
这书吧,例子不错,但是章节布局还有待好好斟酌一下.
0 有用 小马客官 2012-07-11 11:06:51
For someone who works in computer graphics and related fields, this book is an ideal introduction to matrix analysis. Good book!
0 有用 hyiyr 2022-12-04 16:14:12 重庆
对个人来说,这本书就是一座高峰,奇高无比的险峰(个人智力平庸)!第一次拿到这本书,就觉得这本书太数学化了,不适合非理工科的自学。后来,转头学了Gilbert Strang的那本入门书籍。Gilbert 的书学得差不多了再来看这本书,还是感觉非常难,特别是证明这块儿。从证明可看出来,这本书的作者功力不是一般的深厚!我接触这本书差不多有7年的样子了。前前后后差不多看了10来遍了。但是每次看,都有所收获... 对个人来说,这本书就是一座高峰,奇高无比的险峰(个人智力平庸)!第一次拿到这本书,就觉得这本书太数学化了,不适合非理工科的自学。后来,转头学了Gilbert Strang的那本入门书籍。Gilbert 的书学得差不多了再来看这本书,还是感觉非常难,特别是证明这块儿。从证明可看出来,这本书的作者功力不是一般的深厚!我接触这本书差不多有7年的样子了。前前后后差不多看了10来遍了。但是每次看,都有所收获。总的来书,这本书非常不错! (展开)
1 有用 泰能 2020-11-13 22:17:55
很好,就是定位有点不清楚,入门strang更好,想深入lax更好,是很好的工具书了。
0 有用 尘涌酱 2020-08-10 16:41:04
简明易懂
1 有用 林同学 2020-08-04 09:21:43
这本书可以说是这个领域不可多得的好书,尤其对我这种不是数学专业的人。尤其讲特征值那一章,把矩阵函数那一套讲的很清楚,还有案例。然后观点似乎也挺高的,很多地方应该是采用了泛函分析的一些思想。总之一句话,牛逼。
0 有用 Painkiller 2020-03-19 00:01:50
矩阵和线代 我真的学过这些吗……