Introduction to Linear Algebra, 5/e (2016)

Gilbert Strang

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商品描述

Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'.

 

This new fifth edition has become more than a textbook for the basic linear algebra course. That is its first purpose and always will be. The new chapters about applications of the SVD, probability and statistics, and Principal Component Analysis in finance and genetics, make it also a textbook for a second course, plus a resource at work. Linear algebra has become central in modern applied mathematics. This book supports the value of understanding linear algebra.

 

Introduction to Linear Algebra, Fifth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by eight applications: differential equations in engineering, graphs and networks, statistics, Fourier methods and the FFT, linear programming, computer graphics, cryptography, Principal Component Analysis, and singular values.

 

Audience: Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject. This text is for readers everywhere, with support from the websites and video lectures. Every chapter begins with a summary for efficient review.

 

Contents: Chap. 1: Introduction to Vectors; Chap. 2: Solving Linear Equations; Chap. 3: Vector Spaces and Subspaces; Chap. 4: Orthogonality; Chap. 5: Determinants; Chap. 6: Eigenvalues and Eigenvectors; Chap. 7: Singular Value Decomposition; Chap. 8: Linear Transformations; Chap. 9: Complex Vectors and Matrices; Chap. 10: Applications; Chap. 11: Numerical Linear Algebra; Chap. 12: Linear Algebra in Probability and Statistics; Matrix Factorizations; Index; Six Great Theorems.

商品描述(中文翻譯)

Gilbert Strang的教科書改變了學習線性代數的整體方法,從抽象的向量空間轉向具體的四個基本子空間的實例:A的列空間和零空間,以及A'的列空間和零空間。

這本新的第五版不僅僅是基礎線性代數課程的教科書,這是它的首要目的,並且將一直如此。關於奇異值分解(SVD)、概率和統計以及金融和遺傳學中的主成分分析的新章節,使其成為第二門課程的教科書,同時也是工作中的資源。線性代數已成為現代應用數學的核心。這本書支持理解線性代數的價值。

《線性代數導論,第五版》包括挑戰性問題,以補充在先前版本中受到高度讚揚的復習問題。基礎課程後面有八個應用領域:工程中的微分方程、圖形和網絡、統計學、傅立葉方法和快速傅立葉變換、線性規劃、計算機圖形學、密碼學、主成分分析和奇異值。

數以千計的大學和高中教師正在使用這本書,它真正解釋了這一關鍵主題。這本書適合全球讀者,並且有網站和視頻講座提供支持。每章開始時都有一個總結,以便進行高效的復習。

內容包括:第1章:向量導論;第2章:解線性方程組;第3章:向量空間和子空間;第4章:正交性;第5章:行列式;第6章:特徵值和特徵向量;第7章:奇異值分解;第8章:線性變換;第9章:複向量和矩陣;第10章:應用;第11章:數值線性代數;第12章:概率和統計中的線性代數;矩陣分解;索引;六個重要定理。