Elementary Linear Algebra, 8/e (Metric Edition)(IE-Paperback) (初等線性代數（第八版）)

Ron Larson

Elementary Linear Algebra, 8/e (Metric Edition)(IE-Paperback)

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商品描述

ELEMENTARY LINEAR ALGEBRA, 8E, INTERNATIONAL METRIC EDITION's clear, careful, and concise presentation of material helps you fully understand how mathematics works. The author balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. To engage you in the material, a new design highlights the relevance of the mathematics and makes the book easier to read. Data and applications reflect current statistics and examples, demonstrating the link between theory and practice. The companion website LarsonLinearAlgebra.com offers free access to multiple study tools and resources. CalcChat.com offers free step-by-step solutions to the odd-numbered exercises in the text. 

商品描述(中文翻譯)

《初等線性代數，第8版，國際度量版》清晰、細心且簡潔的呈現方式，幫助您完全理解數學的運作方式。作者在理論、例子、應用和幾何直覺之間取得平衡，打造出一個完整、逐步學習的系統。為了讓您更加投入學習，新的設計突顯了數學的相關性，使書籍更易於閱讀。數據和應用反映了當前的統計和例子，展示了理論與實踐之間的聯繫。附帶的網站LarsonLinearAlgebra.com提供免費的多種學習工具和資源。CalcChat.com提供免費的逐步解答本書奇數編號的習題。

目錄大綱

1. SYSTEMS OF LINEAR EQUATIONS.
Introduction to Systems of Equations. Gaussian Elimination and Gauss-Jordan Elimination. Applications of Systems of Linear Equations.
2. MATRICES.
Operations with Matrices. Properties of Matrix Operations. The Inverse of a Matrix. Elementary Matrices. Markov Chains. Applications of Matrix Operations.
3. DETERMINANTS.
The Determinant of a Matrix. Evaluation of a Determinant Using Elementary Operations. Properties of Determinants. Applications of Determinants.
4. VECTOR SPACES.
Vectors in Rn. Vector Spaces. Subspaces of Vector Spaces. Spanning Sets and Linear Independence. Basis and Dimension. Rank of a Matrix and Systems of Linear Equations. Coordinates and Change of Basis. Applications of Vector Spaces.
5. INNER PRODUCT SPACES.
Length and Dot Product in Rn. Inner Product Spaces. Orthogonal Bases: Gram-Schmidt Process. Mathematical Models and Least Squares Analysis. Applications of Inner Product Spaces.
6. LINEAR TRANSFORMATIONS.
Introduction to Linear Transformations. The Kernel and Range of a Linear Transformation. Matrices for Linear Transformations. Transition Matrices and Similarity. Applications of Linear Transformations.
7. EIGENVALUES AND EIGENVECTORS.
Eigenvalues and Eigenvectors. Diagonalization. Symmetric Matrices and Orthogonal Diagonalization. Applications of Eigenvalues and Eigenvectors.
8. COMPLEX VECTOR SPACES (online).
Complex Numbers. Conjugates and Division of Complex Numbers. Polar Form and Demoivre’s Theorem. Complex Vector Spaces and Inner Products. Unitary and Hermitian Spaces.
9. LINEAR PROGRAMMING (online).
Systems of Linear Inequalities. Linear Programming Involving Two Variables. The Simplex Method: Maximization. The Simplex Method: Minimization. The Simplex Method: Mixed Constraints.
10. NUMERICAL METHODS (online).
Gaussian Elimination with Partial Pivoting. Iterative Methods for Solving Linear Systems. Power Method for Approximating Eigenvalues. Applications of Numerical Methods.

目錄大綱(中文翻譯)

1. 線性方程組。
- 介紹方程組。高斯消去法和高斯-喬登消去法。線性方程組的應用。
2. 矩陣。
- 矩陣運算。矩陣運算的性質。矩陣的逆。初等矩陣。馬可夫鏈。矩陣運算的應用。
3. 行列式。
- 矩陣的行列式。使用初等操作求行列式的值。行列式的性質。行列式的應用。
4. 向量空間。
- Rn 中的向量。向量空間。向量空間的子空間。生成集和線性獨立性。基底和維度。矩陣的秩和線性方程組。座標和基底變換。向量空間的應用。
5. 內積空間。
- Rn 中的長度和內積。內積空間。正交基：格拉姆-施密特過程。數學模型和最小二乘分析。內積空間的應用。
6. 線性變換。
- 線性變換的介紹。線性變換的核和值域。線性變換的矩陣表示。過渡矩陣和相似性。線性變換的應用。
7. 特徵值和特徵向量。
- 特徵值和特徵向量。對角化。對稱矩陣和正交對角化。特徵值和特徵向量的應用。
8. 複數向量空間（線上）。
- 複數。共軛和複數的除法。極坐標形式和德莫弗定理。複數向量空間和內積。酉空間和共軛轉置。
9. 線性規劃（線上）。
- 線性不等式系統。涉及兩個變量的線性規劃。單純形法：最大化。單純形法：最小化。單純形法：混合約束。
10. 數值方法（線上）。
- 帶部分選主元的高斯消去法。迭代法求解線性系統。求近似特徵值的冪法。數值方法的應用。

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