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An Introduction to Linear Algebra ( 线性代数导论 ）

An Introduction to Linear Algebra ( 线性代数导论 ）. 郑伟诗 Wei-Shi Jason Zheng wszheng@ieee.org http://sist.sysu.edu.cn/~zhwshi/. 简单自我介绍. 研究方向：机器视觉与智能学习 副教授，中大百人计划 （ 2011 ） 广东省引进创新科研团队计算科学科研团队核心成员 （如果你喜欢高性能计算，记得我们） 研究组： 信科院图像理解与模式识别研究组：赖剑煌 院长 引进创新团队：许跃升教授（千人计划）. 机器视觉. 视觉信息.

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An Introduction to Linear Algebra ( 线性代数导论 ）

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  1. An Introduction to Linear Algebra (线性代数导论） 郑伟诗 Wei-Shi Jason Zheng wszheng@ieee.org http://sist.sysu.edu.cn/~zhwshi/ 10/20/2014, Page 1

  2. 简单自我介绍 • 研究方向：机器视觉与智能学习 • 副教授，中大百人计划 （2011） • 广东省引进创新科研团队计算科学科研团队核心成员 （如果你喜欢高性能计算，记得我们） • 研究组： • 信科院图像理解与模式识别研究组：赖剑煌 院长 • 引进创新团队：许跃升教授（千人计划） 10/20/2014, Page 2

  3. 机器视觉 视觉信息 这人是谁，他/她在做什么，周边什么环境，发生了什么事，……. ？ 机器人能像人类那样理解获取的视觉信息吗？ 3

  4. 高性能机器学习算法

  5. Linear Algebra • An example • In a two-dimensional, the force in physics can be represented by its orientations and the strength of this force (x,y,r) r (x,y), x2+y2=1 10/20/2014, Page 5

  6. Linear Algebra • 线性代数 • 现代线性代数已经扩展到研究任意或无限维空间。一个维数为 n 的向量空间叫做 n 维空间。在二维和三维空间中大多数有用的结论可以扩展到这些高维空间。 • 比如，在经济学中可以使用 8 维向量来表示 8 个国家的国民生产总值（GNP）。当所有国家的顺序排定之后，比如 (中国, 美国, 英国, 法国, 德国, 西班牙, 印度, 澳大利亚)，可以使用向量 (v1, v2, v3, v4, v5, v6, v7, v8) 显示这些国家某一年各自的 GNP。这里，每个国家的 GNP 都在各自的位置上。 • 图像识别：人脸识别 10/20/2014, Page 6

  7. Linear Algebra: for what? • How many dimension? • M-theory: 11 dimension (http://en.wikipedia.org/wiki/M-theory) 10/20/2014, Page 7

  8. Linear Algebra • Illumination (光照) 10/20/2014, Page 8

  9. Linear Algebra • Illumination (光照) 10/20/2014, Page 9

  10. Linear Algebra • Illumination Cone 10/20/2014, Page 10

  11. Linear Algebra • Localized Facial Features （Nature 1999) 10/20/2014, Page 11

  12. Linear Algebra • Dimension Reduction (Science 2000) 10/20/2014, Page 12

  13. Linear Algebra • Super-Resolution (IEEE Trans. on SMC-C,2005) 10/20/2014, Page 13

  14. More General Problem • A linear system • A system of m linear equations in n unknowns • Is there any solution for the above system? None? Unique? Finite? Infinite? • How to solve it generally? • How to describe the solution space? 10/20/2014, Page 14

  15. Linear Algebra • Example: • What is its solution? 10/20/2014, Page 15

  16. Linear Algebra • Linear Algebra studies vector spaces, also called linear spaces. • It also studies linear functions that input one vector and output another. Such functions are called linear maps (or linear transformations or linear operators) and can be represented by matrices if a basis is given. • Matrix theory is a part of linear algebra. 10/20/2014, Page 16

  17. Course Arrangement (课程安排) • 1. Teaching Arrangement： • 17 Weeks • The Midterm Examination: One week • The Final Examination: Around Early January 2013 • 2. Exercise Class(习题课)： • Every two week • By PhD Student, Mr. Yuanlong Li (李元龙) • Homework + Some parts of the book • Starting from the third week 10/20/2014, Page 17

  18. Course Arrangement (课程安排) • 3. About My Teaching • Formally use English and sometimes Chinese • This is a theoretical class. It is important to your future courses such as computer vision, digital image processing, pattern recognition, machine learning, multimedia • If you are with us, let me know. We are not going to leave you behind. • I may give you the answer later. • 以黑板板书为主（推导），ppt为辅（主要是复习和习题课） • You are advised to download my lecture notes. The book is thick and but it is quite good. • The lecture notes can be download here: http://www.eecs.qmul.ac.uk/~jason/sysu/course/linear_algebra/ • The lecture notes will be available before each class 10/20/2014, Page 18

  19. Course Arrangement (课程安排) • 4. Score： • 平时成绩：Homework+考勤（教务处要求）+a small paper +midterm examination • A small paper:2 A4 paper, to tell how linear algebra is used in your our economic life. • Final examination 10/20/2014, Page 19

  20. 过来人的一些唠叨 • 高考不是最后一站，现在是您们未来职业的第一站 • 一开始都是基础课，较理论 • 学习方式与高中不同，现在不会频繁的测验和复习，学习更多靠自觉 • 如果跟不上怎么办？Write me • 人生规划/职业规划 • 本科毕业后工作？你希望的职业是？ • 本科毕业后继续深造：出国？去哪个国家？国内读研？进研究院？ • 无论怎样，都要professional（有专业精神） • 学习成绩不是一切，您们都有各自的特点，现在不再以成绩论英雄 • 但学习成绩是不是可以不要呢？未来的变化谁能完全预测？2+2 • 基本一条：你们现在的职业就是学生，学好基本功是学习本专业的本分 10/20/2014, Page 20

  21. Why Learning Maths • This is to free you for your big dream, probably • Maths would not prevent your success in the future, but may ensure you will succeed • It is a discipline 10/20/2014, Page 21

  22. 蔡元培的一句话：供参考 蔡元培： 大学的学生并不是熬资格，也不是硬记教员的讲义，而是在教员指导之下自动地研究学问的。 10/20/2014, Page 22

  23. Q & A (答疑) • After Class • Email：wszheng@ieee.org • Teaching Assistant：Exercise Class (习题课) • Office Hours：SIST 633B, Tuesday, afternoon, before 5:00PM Write me if you have any advice or questions. It is very appreciated! 10/20/2014, Page 23

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