What are we going to learn Hungyi Lee
- Slides: 18
What are we going to learn? 李宏毅 Hung-yi Lee
System • A system has input and output (function, transformation, operator) Speech Recognition System “How are you” Dialogue System (e. g. Siri, Alexa) “How are you” “I am fine” Communication System “Hello”
Linear System • Linear system have two properties • 1. Persevering Multiplication x Linear System y kx Linear System ky • 2. Persevering Addition x 1 Linear System y 1 x 2 Linear System y 2 x 1+x 2 Linear System y 1+y 2
Linear System x 2 • Linear system have two properties • 1. Persevering Multiplication x Linear System x 2 kx Linear System • 2. Persevering Addition Linear System k 2 x 2
Linear System • Two properties • 1. Persevering Multiplication System • 2. Persevering Addition System
Applications Most system are (assumed to) be linear Linear Input: voltage source, current source output: voltage and current on the load (燈泡、引擎) Circuit + - (大一必修) input Linear System output
Applications Most system are (assumed to) be linear Communication System Linear Channel Transmitter Linear System (大二必修) Receiver
Applications time (大二必修) frequency Fourier Transform Linear System (Transform)
Applications y: A 年 B 月 C 日 N 時的 PM 2. 5 x. K: A 年 B 月 C 日 N – K 時的 PM 2. 5 觀測值 x 1 x 2 x 3 氣象 預報 y Linear system y = w 1 x 1 + w 2 x 2 + w 3 x 3 Where do w 1, w 2 and w 3 come from?
Applications P 336 of Textbook http: //incomebully. com/does-prpagerank-still-matter/
Applications - Page. Rank hyperlink
Applications - Computer Graphics Section 7. 9 of Textbook Linear System http: //www. c-jump. com/bcc/common/Talk 3/Math/Matrices. html
What are we going to learn? Beyond vector in Chapter 6 Chapter 1, Chapter 2, Chapter 3 ? ? ? Does it have solution? vector …… …… vector Linear System 3 6 9 Does it have How to find unique solution? the solution? Determinants ( 行列式) Beyond 3 X 3 Different view from high school
What are we going to learn? … … Simpler Linear System Chapter 4 How to describe this “set”? … … Linear System Change the description Approximation Chapter 7
What are we going to learn? • Chapter 5: Eigen. XXX Enlarge the input Filter Linear System …… …… Linear System Decrease the input
Linear Algebra is Important