Linear Algebra for Everyone (Hardcover)
暫譯: 人人都能懂的線性代數 (精裝版)

Gilbert Strang

Linear Algebra for Everyone (Hardcover)
  • 出版商: Cambridge
  • 出版日期: 2020-12-31
  • 售價: $2,800
  • 貴賓價: 9.5 折 $2,660
  • 語言: 英文
  • 頁數: 368
  • ISBN: 1733146636
  • ISBN-13: 9781733146630
  • 相關分類: 線性代數 Linear-algebra

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商品描述

Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

- Author is a world-renowned teacher of linear algebra who delivers the material in a clear and effective way that students will appreciate
- Uses a highly accessible approach that enables students without a strong mathematics background to understand more advanced topics such as singular value decomposition (SVD)
- Covers topics such as data science and deep learning that show why linear algebra isn't just for mathematicians
- Comes with accompanying video lectures on the MIT OpenCourseWare website, giving students the option to self-study and learn at their own pace

商品描述(中文翻譯)

線性代數已成為各種定量學科人員必須掌握的主題。它不再是數學家和工程師的專屬領域，而是無處不在，任何與數據打交道的人都需要了解更多。這本由著名的線性代數導論（Introduction to Linear Algebra）作者吉爾伯特·斯特朗（Gilbert Strang）教授所撰寫的新書，現在已進入第五版，讓線性代數對每個人都變得可及，而不僅僅是那些具有強大數學背景的人。這本書以更主動的方式開始，首先尋找小矩陣的獨立列，進而引入線性組合、秩和列空間等關鍵概念。接著，它轉向經典主題，包括解線性方程、正交性、線性變換和子空間，所有內容都清晰解釋，並附有許多範例和練習。最後的主要主題是特徵值和重要的奇異值分解（singular value decomposition），並通過對微分方程和圖像壓縮的應用進行說明。最後一章是可選的，探討深度學習背後的理念。

- 作者是世界知名的線性代數教師，以清晰有效的方式傳授材料，學生會感激不已
- 採用高度可及的方法，使沒有強大數學背景的學生能夠理解更高級的主題，如奇異值分解（SVD）
- 涵蓋數據科學和深度學習等主題，顯示線性代數不僅僅是數學家的專利
- 附有MIT OpenCourseWare網站上的視頻講座，讓學生可以選擇自學並按照自己的步調學習

目錄大綱

Preface
1. Vectors and Matrices
2. Solving Linear Equations Ax = b
3. The Four Fundamental Subspaces
4. Orthogonality
5. Determinants and Linear Transformations
6. Eigenvalues and Eigenvectors
7. The Singular Value Decomposition (SVD)
8. Learning from Data
Appendix 1. The Ranks of AB and A + B
Appendix 2. Eigenvalues and Singular Values: Rank One
Appendix 3. Counting Parameters in the Basic Factorizations
Appendix 4. Codes and Algorithms for Numerical Linear Algebra
Appendix 5. Matrix Factorizations
Appendix 6. The Column-Row Factorization of a Matrix
Appendix 7. The Jordan Form of a Square Matrix
Appendix 8. Tensors
Appendix 9. The Condition Number
Appendix 10. Markov Matrices and Perron-Frobenius
Index
Index of Symbols
Six Great Theorems / Linear Algebra in a Nutshell.

目錄大綱(中文翻譯)

Preface

1. Vectors and Matrices

2. Solving Linear Equations Ax = b

3. The Four Fundamental Subspaces

4. Orthogonality

5. Determinants and Linear Transformations

6. Eigenvalues and Eigenvectors

7. The Singular Value Decomposition (SVD)

8. Learning from Data

Appendix 1. The Ranks of AB and A + B

Appendix 2. Eigenvalues and Singular Values: Rank One

Appendix 3. Counting Parameters in the Basic Factorizations

Appendix 4. Codes and Algorithms for Numerical Linear Algebra

Appendix 5. Matrix Factorizations

Appendix 6. The Column-Row Factorization of a Matrix

Appendix 7. The Jordan Form of a Square Matrix

Appendix 8. Tensors

Appendix 9. The Condition Number

Appendix 10. Markov Matrices and Perron-Frobenius

Index

Index of Symbols

Six Great Theorems / Linear Algebra in a Nutshell.

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