Linear Algebra Berlin Chen

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Presentation transcript:

Linear Algebra Berlin Chen Department of Computer Science & Information Engineering National Taiwan Normal University

Linear Algebra Linear algebra is a branch of mathematics and continues to figure prominently in computer science and electrical engineering Computation, geometry, theory, practical applications, to name just a few Simply put, linear algebra is the study of vectors, matrices, vector spaces and linear transformations

Main Objectives Develop the definitions, concepts and theories associated with linear algebra Fundamentals: vectors operations, matrices operations, determinants, Euclidean vector spaces, linear systems, etc. Advanced topics: matrix diagonalization, matrix factorization, linear transforms, numerical methods, practical applications, etc. Learn to make effective use of linear algebra in dealing with practical issues of interest E.g., multimedia (text, speech, music and image) processing

Textbook & Course Website H. Anton, C. Rorres, Elementary Linear Algebra with Supplemental Applications, 11th edition, Wiley, 2014 Website http://www.wiley.com/WileyCDA/WileyTitle/productCd-1118677455.html Course Website http://berlin.csie.ntnu.edu.tw/Courses/LinearAlgebra/2014F-LA_Main.htm

Reference Books D. C. Lay, Linear Algebra and Its Applications, 3rd Updated Edition, Addison Wesley, 2005 Website http://www.laylinalgebra.com/ D. P. Bertsekas, J. N. Tsitsiklis, Introduction to Probability, 2nd Edition, Athena Scientific, 2008 http://www.athenasc.com/probbook.html

Tentative Topic List 1. Systems of Linear Equations and Matrices 2. Determinants 3. Euclidean Vector Spaces 4. General Vector Spaces 5. Eigenvalues and Eigenvectors 6. Inner Product Spaces 7. Diagonalization and Quadratic Forms 8. Linear Transformations

Grading (Tentatively!) Midterm and Final: 45% Quizzes ( 5 times) and Homework: 45% Attendance/Other: 10% TA：洪孝宗同學 (語音實驗室；R208) E-mail: 60047064S@ntnu.edu.tw Tel: 7734-6676

q = 0u1 + 0u2 + 3u3 d1 = 2u1 + 4u2 + 5u3 d2 = 3u1 + 7u2 + 7u3 u3 u1 u2 Information Retrieval (IR): Measuring Degree of Similarity between Query and Documents q = 0u1 + 0u2 + 3u3 d1 = 2u1 + 4u2 + 5u3 d2 = 3u1 + 7u2 + 7u3 u3 7 d1 = 2u1+ 4u2 + 5u3 5 3 d2 = 3u1 + 7u2 + 7 u3 q = 0u1 + 0u2 + 3u3 2 3 u1 4 7 u2