Sang-Gu LEE with Jon-Lark KIM, In-Jae KIM, Namyong LEE,

Ajit KUMAR, Phong VU, Victoria LANG, Jae Hwa LEE

http://matrix.skku.ac.kr/2015-Album/Big-Book-LinearAlgebra-Eng-2015.pdf 

http://matrix.skku.ac.kr/2015-Album/BigBook-LinearAlgebra-2015.pdf   


Linear Algebra with Sage 

 

                               http://matrix.skku.ac.kr/LA-Sage/

LA with Sage  - Introduction (1st Class)  http://youtu.be/Vx1r-y_xIeM

Linear Algebra Lectures by SGLee


(2016) Linear Algebra Lectures at SKKU :   (English Version) (updated on June 11th, 2016)

 

 (English Textbook) http://matrix.skku.ac.kr/2015-Album/Big-Book-LinearAlgebra-Eng-2015.pdf   

 (e-book : Korean) http://matrix.skku.ac.kr/2015-Album/BigBook-LinearAlgebra-2015.pdf  


http://matrix.skku.ac.kr/LA/Ch-1/ 

http://matrix.skku.ac.kr/LA/Ch-2/ 

http://matrix.skku.ac.kr/LA/Ch-3/ 

http://matrix.skku.ac.kr/LA/Ch-4/ 

http://matrix.skku.ac.kr/LA/Ch-6/ 

             http://matrix.skku.ac.kr/2016-album/LA-Sol-Ch-1-2-3-4-6/index.html

             http://matrix.skku.ac.kr/LA-Lab/Solution/

             http://matrix.skku.ac.kr/2016-album/LA-Main-Theorems/index.html

    Midterm Exam :  http://matrix.skku.ac.kr/LA/2016-S-LA-Midterm-Final-Solution.pdf

 

http://matrix.skku.ac.kr/LA/Ch-7/ 

http://matrix.skku.ac.kr/LA/Ch-8/ 

http://matrix.skku.ac.kr/LA/Ch-9/ 

http://matrix.skku.ac.kr/LA/Ch-10/ 


http://matrix.skku.ac.kr/knou-knowls/


LA - first Class - Introduction, (1/2) https://youtu.be/kqn9DYtRqrA 

Chapter 1.

LA Sec 1.1, 1.2,  first Class (2/2)  https://youtu.be/f6eKIuLE-Ko

LA Sec 1.3, Vector Equations of Lines and Planes,  https://youtu.be/zRw2M2nhYCg 

Chapter 2.

LA Sec 2.1, 2.2, Linear System of Equations,  https://youtu.be/WwJR-5yF0oE

Chapter 3.

LA Sec 3.1, 3.2, 3.3, Matrix Algebra, Part 1,  https://youtu.be/6U9pELZZ-fc

LA Sec 3.4, 3.5, 3.6, Subspace, Solution Space, https://youtu.be/HfJSYHhrAHI6

LA Sec 3.7, Special Matrices, https://youtu.be/KjXm5DhEP9U

Chapter 4.

LA Sec 4.1, Determinant,  https://youtu.be/LVUNNmUmo2M

LA Sec 4.2, 4.3. 4.4, Cofactor Expansion, https://youtu.be/R-I8brsJM9M

LA Sec 4.5, Eigenvalues and eigenvectors (화면) https://youtu.be/jJVCKWSOrOw

Chapter 6.

LA Sec 6.1, Linear Transformation, https://youtu.be/3UGA-FCPSlQ

LA Sec 6.2, Geometric Meaning of Linear Transformation, https://youtu.be/59Emwx-I2d8

LA Sec 6.3, Kernel and Range https://youtu.be/v_fV3TGI7kE

LA Sec 6.4, Composite of LT https://youtu.be/YbHpX5I_mMU


Problem Solving (Ch 1.-Ch.10)
LA Problem solving Ch. 1, https://youtu.be/4pneV9Wm_u8

LA Problem solving Ch. 2, https://youtu.be/cxZYR_OwIRo

LA Problem solving Ch. 3, https://youtu.be/ZHzTvuHc9MI

LA Problem solving Ch. 4, 학생발표  2조 https://youtu.be/o52eayUUOnk

LA Problem solving Ch. 6, 학생발표 4조 https://youtu.be/ytNRPS1IkCk

      LA Midterm Review https://youtu.be/Z89XvKXIYeg 

LA Problem solving Ch. 7, 학생발표, https://youtu.be/7SB1hQI-hzM  

LA Problem solving Ch. 8, 학생발표, https://youtu.be/iNVN0-q15to  

LA Problem solving Ch. 9, 학생발표, https://youtu.be/hGoeTDwWlUY

LA Problem solving Ch. 10, 학생발표 https://youtu.be/7ZtxicpdMkw  

 

 Sample Exam : http://matrix.skku.ac.kr/2015-Album/2015-LA-S-Exam-All-Sol.pdf

                 http://matrix.skku.ac.kr/LA/LA-F-EXAM-Solution.pdf

Sample Exam : http://matrix.skku.ac.kr/LA/2016-S-LA-Midterm-Final-Solution.pdf


* Chapter 5. Matrix Model (행렬 모델)

5-1 Power Method: http://youtu.be/CLxjkZuNJXw 

5-2 Cryptography: http://youtu.be/umTIADxsEq8 

5-3 Blackout Game: http://youtu.be/_bS33Ifa29s 

5-4 Markov Chains: http://youtu.be/156ezier6HQ 

5-5 Google Matrix: http://youtu.be/WNUoXLh8i_E 

5-6 Project: http://youtu.be/coNq48CW6Pg 

    - Ch 5 Matrix Model 학생 발표 https://youtu.be/4u9LtmX7lvk 


LA Midterm Review https://youtu.be/Z89XvKXIYeg

 

Chapter 7. Dimension and Subspaces

LA Sec 7.1, Properties of bases and dimensions, https://youtu.be/tZ-zx8oNobM

LA Sec 7.2 Basic spaces of matrix   https://youtu.be/CO7TzhwA-fk

LA Sec 7.3 Rank-Nullity theorem  https://youtu.be/165XEM_qekQ

LA Sec 7.4 and 7.5  Rank theorem and Projection theorem  https://youtu.be/S4SmPxFJzGE  

LA Sec *7.6 Least square solution (https://youtu.be/GwHh5lh5wEs )

LA Sec 7.7 Gram-Schmidt orthonomalization process, https://youtu.be/sMoXeFn4g7E

LA Sec 7.8 QR-Decomposition; Householder transformations (https://youtu.be/gQ7gxTx5f9k)

LA Sec 7.9 Coordinate vectors  https://youtu.be/uGxyI7LGINA

 

 학생 문제 풀이  Section 7-1  http://www.youtube.com/watch?v=BHf1AZjYAdQ

                Section 7-5  http://www.youtube.com/watch?v=BC9qeR0JWis

                Section 7-7  http://youtu.be/ZRa-4MnWb48

                Section 7-9  http://youtu.be/X9VR_0Xnbcc

 

Chapter 8. Diagonalization

LA Sec 8.1 Matrix Representation of LT and 8.2 Similarity and Diagonalization, https://youtu.be/DJwT9f326_Q

LA Sec 8.3 Diagonalization with orthogonal matrix, *Function of matrix, https://youtu.be/aIKl1ScEzf8

LA Sec 8.4 Quadratic forms, https://youtu.be/vgzfkTg7Q5w

LA Sec *8.5 Applications of Quadratic forms (http://youtu.be/cOW9qT64e0g)

LA Sec 8.6 SVD and  Generalized Inverse,  https://youtu.be/AYRR-BEAot8

LA Sec 8.7 Complex eigenvalues and eigenvectors, https://youtu.be/tqWtF8-4emc

LA Sec 8.8 Hermitian, Unitary, Normal Matrices, https://youtu.be/FiP8rU4JsW0

LA Sec *8.9 Linear system of differential equations (https://www.youtube.com/watch?v=c0y5DcNQ8gs)

 

 학생 문제 풀이 Section 8-1 http://youtu.be/Oy7ZbacWDhk  

               Section 8-2 http://www.youtube.com/watch?v=00HeZNTN_vc http://www.youtube.com/watch?v=7g5Du3_D5PQ

               Section 8-3 http://www.youtube.com/watch?v=HSPYrYju1ZY

               Section 8-4 http://youtu.be/aYTuHkNKbB4

               Section 8-5 http://www.youtube.com/watch?v=gWEtJYqvMuQ

               Section 8-6 http://www.youtube.com/watch?v=m7u1-XphQ3s

               Section 8-7 http://youtu.be/jDViGood6VA

               Section 8-8 http://www.youtube.com/watch?v=lEolZQp_55g  http://youtu.be/SJfshBcj_oc http://youtu.be/Ajos-zIx6pA

               Section 8-9 http://www.youtube.com/watch?v=c0y5DcNQ8gs

 

Chapter 9. General Vector Spaces

LA Sec 9.1 Axioms of Vector Space, https://youtu.be/RnKjspG65AM

LA Sec 9.2 Inner product spaces; *Fourier Series, https://youtu.be/J0s8AkP4E38

9.3 Isomorphism, https://youtu.be/WiZZtF0c1hY

 

 학생 문제 풀이 Section 9-1 http://www.youtube.com/watch?v=G3Fek3W9kVg

               Section 9-2 http://www.youtube.com/watch?v=UuSBrN4-4Fc

               Chapter 9   http://www.youtube.com/watch?v=tmzbqK3rZfg http://www.youtube.com/watch?v=Bqablzyb_30

 

Chapter 10. Jordan Canonical Form

10.1 Finding the Jordan Canonical Form with a Dot Diagram (https://youtu.be/8fwPPOg8LW0 )

*10.2 Jordan Canonical Form and Generalized Eigenvectors, https://youtu.be/YrRnCByzxNM  ( https://youtu.be/yJ7n0icjtNA )

 10.3 Jordan Canonical Form and CAS, https://youtu.be/YrRnCByzxNM    (http://youtu.be/LxY6RcNTEE0 )

(학생 문제 풀이, https://youtu.be/y4173MpjoxE ,

  Section 10-1 http://youtu.be/9-G3Fd2xOW0  

 Chapter 10 http://www.youtube.com/watch?v=adWzUKKmO2k

(Math for Big Data, Lecture 10, Finding JCF using Dot Diagram, https://youtu.be/1E3wXN1oZyc)

(Math for Big Data, Lecture 11, Generalized eigenvectors and Matrix Function, https://youtu.be/lK4_Kp6P_N4)

 

...

 Appendix

 

Solution Book for Linear Algebra

  http://matrix.skku.ac.kr/LA-Lab/Solution/     

Project Presentation (Project 발표) http://youtu.be/cxdj7hDWk08

[Sample Exam]

Sample Exam : http://matrix.skku.ac.kr/2015-Album/2015-LA-S-Exam-All-Sol.pdf

Sample Exam : http://matrix.skku.ac.kr/LA/2016-S-LA-Midterm-Final-Solution.pdf

Reference video: http://youtu.be/CLxjkZuNJXw  

http://matrix.skku.ac.kr/CLA-Exams-Sol.pdf ,

http://matrix.skku.ac.kr/2015-album/2015-LA-S-Exam-All-Sol.pdf  

http://matrix.skku.ac.kr/2015-album/2015-LA-F-Midterm-Final-Solution-F.pdf

http://matrix.skku.ac.kr/2012-album/2012-LA-Lectures.htm  

... 


Appendix 

 

| Preface |


This book, ‘Linear Algebra with Sage’, has two goals. The first goal is to explain Linear Algebra with the help of Sage. Sage is one of the most popular computer algebra system(CAS). Sage is a free and user-friendly software. Whenever the Sage codes are possible, we illustrate examples with Sage codes. The second goal is to make the book accessible to everyone in the world freely. Therefore, the pdf file of this book is free to use in class or in person. For commercial use, please contact us.


Linear Algebra is regarded as one of the most important mathematical subjects because it is used not only in natural sciences and engineering applications but also in humanities and social sciences. Nowadays, Linear Algebra is studied most actively in the 21st century.


One of the roles of mathematics in society is to suggest a possible solution by modeling a practical problem as a mathematical problem, by solving it with the idea of a system of linear equations, and by interpreting the solution in the setting of the original problem. The first computer is also based on the linear process. The study and applications of Linear Algebra grew incredibly in the later part of the 20th century.


It is interesting to note that Sylvester and Cayley, inventors of matrices, and Babbage, father of the computer, were mathematicians in the 19th century from United Kingdom. Since then, the study of matrix theory has progressed and contributed to the development of physics by the appearance of infinite dimensions and tensors.


Matrix theory in the United States of America was neglected from the European mathematical society before the Second World War. After that, because the modern computers were built and the numerical power of matrices became very useful, the matrix theory was developed well in the United Sates in the 20th century. The United States has grown as a unique super power in both theories and experiments of sciences.


| How to use Lab |    https://www.youtube.com/watch?v=V0xJvW-YjWs


[CAS-Geogebra] http://www.geogebratube.org/student/b121550

[CAS-LA] http://matrix.skku.ac.kr/Lab-book/Sage-Lab-Manual-2.htm

[CAS-Sage] http://matrix.skku.ac.kr/knou-knowls/Sag-Ref.htm 

 

 



Linear Algebra CONTENTS,       
(Lecture and Solutions)  
(Korean Version)

Chapter 1. 벡터

*1.1 공학과 수학에서의 벡터: n-차원공간

     (http://youtu.be/85kGK6bJLns, http://youtu.be/fbCMyh-iDCQ)

             <http://matrix.skku.ac.kr/2007-CLA-Credu/01_01/main.html>

*1.2 내적과 직교

   (http://youtu.be/g55dfkmlTHE , http://youtu.be/sEFj_7t_bqc)

 1.3 직선과 평면의 벡터방정식

  (http://youtu.be/YB976T1w0kE, http://youtu.be/avVJfeEoeVs )

                (웹브라우저는 IE 보다는 크롬을 이용하기를 권합니다.)

 

 선형대수학은 모든 분야에서 널리 이용되기 때문에 자연계는 물론 인문사회계의 학생에게도 가장 중요한 수학과목의 하나로 여겨진다. 본 교재는 자연계, 공학계, 사회과학계의 학생을 대상으로 한 학기 또는 일 년에 현대선형대수학의 입문과 응용 및 공학적 도구의 이용에 대한 폭넓은 지식을 제공하는 것을 목표로 한다.

 본 교재는 이상구 교수가 지난 20년간 강의하며 개발한 강의 자료와 원고, 웹 콘텐츠, 논문과 공학적 도구 등 강의 관련 자료를 바탕으로 마련되었으며, 특히 이 책은 미국 과학재단(NSF)과 국제 선형대수학회(International Linear Algebra Society, http://www.ilasic.math.uregina.ca/iic), 미국수학회, 미국수학교육학회가 연계하여 21세기에 맞는 선형대수학 교재가 갖추어야 할 내용과 새로운 전개 방법을 제시한 Linear Algebra Curriculum Study Group (LACSG)의 가이드라인에 맞추어 학생들이 전통과 첨단이 조화된 선형대수학의 전체적인 흐름을 알고, 쉽게 내용을 이해한 후 실제 문제를 이론적으로 또 실제적으로 해결할 수 있는 능력을 갖추도록 모든 내용을 담아 쉽게 썼다.

 이상구 교수가 원고를 써서 가제본을 만든 후 실제 수업에 1년간 사용하면서 김덕선-설한국-이재화 박사는 Sage 소프트웨어의 적용과 Technology 부분의 새로운 문제를 보태고 다양한 학교 및 전공의 학생에게 맞도록 윤문하고 오타를 찾으며 추가된 새로운 접근방법의 효과성을 확인하였다. 교재에 보태어 양방향 학습이 가능하도록 저자가 제공하는 홈페이지에서는 강의계획서의 예, 동영상 강의 및 문제풀이와 샘플 시험 및 정의집과 다양한 참고자료를 담았다.

 Linear Algebra 

 (선형대수학)  by SGLee

 http://matrix.skku.ac.kr/2012-album/2012-LA-Lectures.htm

     http://sage.skku.edu/static/mc.html (행렬계산기) 동영상설명

     2012-Visual Math with Sage

Chapter 2. 선형연립방정식

 2.1 선형연립방정식

 2.2 Gauss 소거법과 Gauss-Jordan 소거법

*2.3 선형연립방정식의 응용

    Quiz :

http://matrix.skku.ac.kr/2012-Album/CLA-Spring-Exams-Sol.pdf

Chapter 3. 행렬과 행렬대수

 3.1 행렬연산

 3.2 역행렬

 3.3 기본행렬과 역행렬

 3.4 부분공간과 일차독립

 3.5 선형연립방정식의 해집합과 행렬

 3.6 특수행렬들(Special matrices)

*3.7 LU-분해

 

Chapter 4. 행렬식

 4.1 행렬식의 정의와 기본정리

 http://matrix.skku.ac.kr/2012-Album/CLA_Book-Model/CLA_0516-Model.html

 4.2 여인자 전개와 행렬식의 응용

 4.3 크래머 공식

*4.4 행렬식의 응용

 4.5 고유값과 고유벡터

 

*Chapter 5. 행렬모델 (Matrix Model)

    5-1 Power Method: http://youtu.be/CLxjkZuNJXw

    5-2 Cryptography: http://youtu.be/umTIADxsEq8

    5-3 Blackout Game: http://youtu.be/_bS33Ifa29s

    5-4 Markov Chains: http://youtu.be/156ezier6HQ

    5-5 Google Matrix: http://youtu.be/WNUoXLh8i_E

    5-6 Project: http://youtu.be/coNq48CW6Pg

 

Chapter 6. 선형변환

 6.1 함수(변환)로서의 행렬

 6.2 선형연산자의 기하학적 의미

 6.3 핵과 치역

 6.4 선형변환의 합성과 가역성

*6.5  컴퓨터 그래픽

 

Chapter 7. 차원과 부분공간

 7.1 기저와 차원의 성질

     http://matrix.skku.ac.kr/2007-CLA-Credu/07_01/main.html

 7.2 행렬이 갖는 기본공간들

 7.3 차원정리

 7.4 Rank 정리

 7.5 정사영(Projection) 정리

*7.6 최소제곱해(least square solution)

 7.7 Gram-Schmidt의 정규직교화과정

*7.8 QR-분해; Householder transformations

 7.9 좌표벡터

     http://matrix.skku.ac.kr/2007-CLA-Credu/07_09/main.html

Chapter 8. 행렬의 대각화

 8.1 선형변환의 행렬표현

 8.2 닮음과 행렬의 대각화

 8.3 직교대각화, *행렬 함수

 8.4 이차형식

*8.5 이차형식의 응용

*8.6 SVD와 일반화된 역행렬

 8.7 복소고유값과 고유벡터

 8.8 Hermitian, 유니타리, 정규행렬

*8.9 선형연립미분방정식

 

Chapter 9. 일반벡터공간

 9.1 벡터공간의 공리

 9.2 내적공간; *푸리에 급수

 9.3 동형사상(Isomorphism)

 

Chapter 10. Jordan 표준형(with Sage)

 10.1 점도표를 이용한 Jordan 표준형 구하기

*10.2 Jordan 표준형과 일반화된 고유벡터

 10.3 Jordan 표준형과 컴퓨터 활용

          http://matrix.skku.ac.kr/2012-mobile/E-CLA/10-1.html

          http://matrix.skku.ac.kr/2012-mobile/E-CLA/10-1-ex.html

 

Final Exam:

      http://matrix.skku.ac.kr/2013-Album/CLA-2012-Fall-Final-sol-F/CLA-2012-Fall-Final-sol-F.html

   SKKU LA 2009- Final Exam

 MATRIX THEORY :

    http://matrix.skku.ac.kr/OCW-MT/index.htm

 Solutions : 

  http://matrix.skku.ac.kr/2010-Album/2010-MT-all-Solution-v1-sglee/2010-MT-all-Solution-v1-sglee.html

 

Internet resources :

Sage-Reference: Link
Sage Tutorial:
Link
2011-How to use Sage 2:
Link
William Stein demos sage math:
Link
2011-Mobile Math with Sage:
Link
Sage Interact / ODE and Mandelbrot:
Link
Sage Multivariable Calculus (1 of 2) by Travis:
Link
Sage Multivariable Calculus (2 of 2) by Travis:
Link
국내대학강의
-성균관대학교-선형대수학 동영상 강의: Link

http://matrix.skku.ac.kr/2012-LAwithSage/interact
http://matrix.skku.ac.kr/2012-sage/sage-la

http://matrix.skku.ac.kr/2011-sage/sage/clawithsage.html

http://matrix.skku.ac.kr/2008-Album/CLA-QnA-YHLee.htm

http://youtu.be/CbfJYPCkbm8

http://bkmath.skku.ac.kr/bk21

http://matrix.skku.ac.kr/sglee

http://matrix.skku.ac.kr/2013-Calculus-Sage/Cal-lab-0-3/cal-lab-ch0to3.htm

http://matrix.skku.ac.kr/2013-Calculus-Sage/Web-Cover/CH-0-Cover.pdf

http://matrix.skku.ac.kr/sglee/LADef/defin.htm (정의집)
http://matrix.skku.ac.kr/2008-Lecture/LAA-sglee
(교재 1)
http://matrix.skku.ac.kr/CLAMC
(교재 2)
http://matrix.skku.ac.kr/sage
(공개한 소스)

http://sage.skku.edu (무료 공학용 계산기 : Single Cell 서버)
http://matrix.skku.ac.kr/LA-Lab/SKKU-Cell-Epsilon-Delta.html

http://matrix.skku.ac.kr/LA-Lab/LA-1-CAS-2.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-2-2.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-3.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-4.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-5.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-6.html

http://matrix.skku.ac.kr/LA-Lab/LA-C-7.html

국제선형대수학회 :http://matrix.skku.ac.kr/2010-Album/2010-06-ILAS.html

   * 수학과와 통계학과의 소개

    http://matrix.skku.ac.kr/2013-Album/Math-Stat-Intro.htm

Main Author : Sang-Gu Lee

 

Co-Authors : Jaehwa Lee, Duk-Sun Kim

 

 

 

          2013.

 

   

Made by Prof. Sang-Gu LEE(sglee at skku.edu) with Shaowei SUN and Kyungwon KIM

Copyright at Sungkyunkwan University, March 2013