具體描述
《Linear Algebra》用英語寫成，包含多項式和綫性代數的基本內容，邏輯清晰，章節安排自然閤理，有近550道配套習題，許多習題十分新穎。主要內容包括：整數和多項式，綫性方程組，綫性映射，矩陣和行列式，綫性空間和綫性映射，綫性變換，歐幾裏得空間，綫性型，雙綫性型以及二次型。《Linear Algebra》適閤數學係本科生作為高等代數教材使用，也可作為雙語教學和綫性代數的參考教材。
著者簡介
圖書目錄
1 Integers and Polynomials
1.1 Integers
1.2 N'umber Fields
1.3 Polynomial
1.4 Polynomial Functions and Roots
1.5 Polvnomials over Rational Number Field
1.6 Polynomials of Several Variables
1.7 Symmetric Polynomials
1.8 Exercises
2 Systems of Linear Equations
2.1 Systems of Linear Equations and Elimination
2.2 Vectors
2.3 Matrices
2.4 Structure of Solutions of A System of Linear Equations
2.5 Exercises
3 Linear Maps, Matrices and Determinants
3. 1 Linear Maps of Vector Spaces and Matrices
3.2 Operations of Linear Maps and Matrices
3.3 Partitioned Matrices
3, 4 Elementary Matrices and Invertible Matrices
3.5 Determinants
3.5.1 Permutation and Determinant
3.5.2 Properties of Determinant
3.5.3 Expansion of Determinant
3.5.4 Applications of Determinant
3.6 Exercises
4 Linear Spaces and Linear Maps
4. 1 Linear Spaces
4.2 Dimension, Basis, Coordinates
4.3 Basis Change and Coordinate Transformations
4.4 Linear Maps and Isomorphism
4.5 Matrices of Linear Maps
4.6 Subspaces and Direct Sum
4.7 Space Decomposition and Partitioned Matrices
4.8 Exercises
5 Linear Transformations
5.1 Linear Transformations
5.2 Similarity of Matrices
5.3 ),-Matrices
5.4 Eigenvalues, Eigenvectors and Characteristic Polynomials
5.5 Invariant Subspaces
5.6 Equivalence of λ-matrices
5.7 Invariant Factors and Elementary Divisors
5.8 Condition for Similarity of Matrices
5.9 Jordan Canonical Forms of Matrices
5.10 Rat iona! Canonical Forms of Matrices
5.11 Exercises
6 Euclidean Spaces
6.1 Inner Product and Basic Properties
6.2 Orthogonal Bases and Schmidt Orthonormalization
6.3 Subspaces and Orthogonal Complements
6.4 Isometry and Orthogonal Transformations
6.5 Symmetric Matrices and Symmetric Transformations
6.6 The Method of Least Squares——System of Linear Equations
Revisited
6.7 A Brief Introduction to Unitary Spaces
6.8 Exercises
7 Linear Forms, Bilinear Forms and Quadratic Forms
7.1 Linear Forms and the Dual Space
7.2 Bilinear Forms
7.3 Symmetric Bilinear Forms
7.4 Quadratic Forms
7.5 Quadratic Forms over Real and Complex Number Fields
7.6 Positive Definite Quadratic Forms over Real Number Field
7.7 Exercises
Bibliography
Index
· · · · · · (收起)
1.1 Integers
1.2 N'umber Fields
1.3 Polynomial
1.4 Polynomial Functions and Roots
1.5 Polvnomials over Rational Number Field
1.6 Polynomials of Several Variables
1.7 Symmetric Polynomials
1.8 Exercises
2 Systems of Linear Equations
2.1 Systems of Linear Equations and Elimination
2.2 Vectors
2.3 Matrices
2.4 Structure of Solutions of A System of Linear Equations
2.5 Exercises
3 Linear Maps, Matrices and Determinants
3. 1 Linear Maps of Vector Spaces and Matrices
3.2 Operations of Linear Maps and Matrices
3.3 Partitioned Matrices
3, 4 Elementary Matrices and Invertible Matrices
3.5 Determinants
3.5.1 Permutation and Determinant
3.5.2 Properties of Determinant
3.5.3 Expansion of Determinant
3.5.4 Applications of Determinant
3.6 Exercises
4 Linear Spaces and Linear Maps
4. 1 Linear Spaces
4.2 Dimension, Basis, Coordinates
4.3 Basis Change and Coordinate Transformations
4.4 Linear Maps and Isomorphism
4.5 Matrices of Linear Maps
4.6 Subspaces and Direct Sum
4.7 Space Decomposition and Partitioned Matrices
4.8 Exercises
5 Linear Transformations
5.1 Linear Transformations
5.2 Similarity of Matrices
5.3 ),-Matrices
5.4 Eigenvalues, Eigenvectors and Characteristic Polynomials
5.5 Invariant Subspaces
5.6 Equivalence of λ-matrices
5.7 Invariant Factors and Elementary Divisors
5.8 Condition for Similarity of Matrices
5.9 Jordan Canonical Forms of Matrices
5.10 Rat iona! Canonical Forms of Matrices
5.11 Exercises
6 Euclidean Spaces
6.1 Inner Product and Basic Properties
6.2 Orthogonal Bases and Schmidt Orthonormalization
6.3 Subspaces and Orthogonal Complements
6.4 Isometry and Orthogonal Transformations
6.5 Symmetric Matrices and Symmetric Transformations
6.6 The Method of Least Squares——System of Linear Equations
Revisited
6.7 A Brief Introduction to Unitary Spaces
6.8 Exercises
7 Linear Forms, Bilinear Forms and Quadratic Forms
7.1 Linear Forms and the Dual Space
7.2 Bilinear Forms
7.3 Symmetric Bilinear Forms
7.4 Quadratic Forms
7.5 Quadratic Forms over Real and Complex Number Fields
7.6 Positive Definite Quadratic Forms over Real Number Field
7.7 Exercises
Bibliography
Index
· · · · · · (收起)
讀後感
評分
評分
評分
評分
評分
用戶評價
评分
專業的教材，可惜我隻看瞭習題????
评分引入的方式還可以的，能夠加深對矩陣的一些理解。
评分當年自印的教材齣書瞭。比較好的入門教材，對於剛剛進入大學的數學係學生來說，無論是數學訓練還是英文錶達都非常有幫助。
评分當年自印的教材齣書瞭。比較好的入門教材，對於剛剛進入大學的數學係學生來說，無論是數學訓練還是英文錶達都非常有幫助。
评分習題部分真的很好！
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