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/ Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 1

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） Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 2

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

高性能机器学习算法

Linear Algebra An example (x,y,r) r (x,y), x2+y2=1 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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 5

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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 6

Linear Algebra: for what? How many dimension? M-theory: 11 dimension (http://en.wikipedia.org/wiki/M-theory) Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 7

Linear Algebra Illumination (光照) Wei-Shi Zheng 3/9/2017, Page 8 wszheng@ieee.org 3/9/2017, Page 8

Linear Algebra Illumination (光照) Wei-Shi Zheng 3/9/2017, Page 9 wszheng@ieee.org 3/9/2017, Page 9

Linear Algebra Illumination Cone Wei-Shi Zheng 3/9/2017, Page 10 wszheng@ieee.org 3/9/2017, Page 10

Linear Algebra Localized Facial Features （Nature 1999) Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 11

Linear Algebra Dimension Reduction (Science 2000) Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 12

Linear Algebra Super-Resolution (IEEE Trans. on SMC-C,2005) Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 13

A system of m linear equations in n unknowns 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? Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 14

Linear Algebra Example: What is its solution? Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 15

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. Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 16

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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 17

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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 18

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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 19

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 人生规划/职业规划 无论怎样，都要professional（有专业精神） 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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 20

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 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 21

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。 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。 Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 22

Write me if you have any advice or questions. 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! Wei-Shi Zheng wszheng@ieee.org 3/9/2017, Page 23