Matrix Theory - Sang-Gu Lee

Linear Algebra (?�?�?�?�?�) by SGLee

[New] ?�?�?�?�?� Interactive ?�?��?(GeoGebra+Sage+강?�록+?�?�?�)

Index	Contents
1	?�?� ?�립방정?� Linear equations and matrices
2	?�칼??�?Scalar multiplication
3	벡터의 ??Vector addition
4	?�?�의 �?Matrix product
5	?�?�?? Inverse matrices
6	?�?�을 ?�용한 ?�?�시?�템 Cryptography
7	?�백�??�?� ?�?�?�?�?� Blackout Game and LA
8	?��??�?� ?�??Determinant
9	?�?�?� 방정?� Vector equations of planes
10	?�?�영 Projection
11	최?�?�곱�??� Least square solutions
12	고?�값�?고?�벡�?/span> Eigenvalues and Eigenvectors
13	?�칭변?� Linear transformations
14	?�칭변?��??�?�영변?� Linear transformations
15	?�?�?� ?�축 및 ?�창 Linear transformations
16	?�미�??� ?�축 및 ?�창 Linear transformations

17	층�?�?변?� Linear transformations
18	?�극기?� ?�?� Linear transformations

19	보�?법 Interpolation
20	?�차?�?� Quadratic Forms
21	?�리?� 급?� Fourier Series
22	조르???�준?� Jordan Canonical Forms
23	?�??계?�기 Matrix Calculator
24	미적분?� 계?�기 Calculus, CAS
25	그래??/a> , 3D

26	마코?�체�?/a>
27	?�면의 방정?�

28	Linear Combination(?�차결�?
29	?�?��??�

30	Volume of Parallelepiped
31	Power-Method-Algorithm ?� ?�?� 비교

32	Gram-Schmidt o.n. Processiped
33

Syllabus
교과목명	?�?�?�?�?�	?�?�번??/SPAN>	GEDB003-42
?�용언�?/SPAN>	English	?�?�구�?	교?�.기�?
?�강?�?�?�부	all	?�수구�?	교?�.기�?
?�?�/?�간	3?�?� / 3?�간	?��?구�? ?�?�/?��?/SPAN>	201/ ?��?/P>
강?�??/SPAN>	기�??�문�? 1�?017?�51155?�	?�?�?�간	?�,�?10:30~11:45
?�당�??� 명	?�상�?교?�	?�락�?(?�구??	031-290-7025
E-Mail	sglee@skku.edu
교과목 개?�	We will cover : Vectors, geometric, norm, vector addition, dot product, equality, application of angle between vectors as measure of genetic distance Systems of linear equations and Gauss-Jordan elimination, Matrices, inverses, diagonal, triangular, symmetric, trace, geographical distribution, probability matrices, and application to colour. LT. Determinants, evaluation by row operations and Laplace expansion, properties, vector cross products, eigenvalues and eigenvectors, Differential equations, system of first order linear equations, applications to population dynamics, linear second order equations. Jordan canonical Forms. You may refer : http://matrix.skku.ac.kr/CLAMC/index.html http://matrix.skku.ac.kr/2011-sage/sage-la/ http://www.youtube.com/watch?v=97qI2yQC5Gs
교과목 목표	We will discuss many interesting problems from textbook and other in English. This will be an introduction to linear algebra, including matrix operations, systems of linear equations, vector spaces, subspaces, bases and linear independence, eigenvalues and eigenvectors, diagonalization of matrices, linear transformations, determinants. If you have any conflict with it, I would recommend to take other class. All Quiz problems will be given in English.

Linear Algebra with Sage (?�?�?� 강?�)

??Made by Prof. SGLee at Sungkyunkwan Univ.

SKKU Linear Algebra with Sage
강좌명		?�?�?�?�?�			?�당�??�		sglee@skku.edu
Ch.	주제		section	?��?/SPAN>		?�?�?� 강?�?�료
0				Preface		http://youtu.be/CbfJYPCkbm8
				Introduction of CAS		http://youtu.be/0SQpiNe2LU8
1	벡�?/P>		1-1	Vector		http://youtu.be/85kGK6bJLns
			1-2	Norm		http://youtu.be/g55dfkmlTHE
			1-3	Vector Equations		http://youtu.be/YB976T1w0kE
2	?�?�?�립방정?�		2-1	LSE		http://youtu.be/AAUQvdjQ-qk
			2-2	RREF		http://youtu.be/HSm69YigRr4
			2-3	Appl of LSE		http://youtu.be/G790BLDSK5g
3	?�?�과 ?�?�대?�		3-1	Matrix		http://youtu.be/JdNnHGdJBrQ
			3-2	Inverse Matrix		http://youtu.be/yeCUPdRx7Bk
			3-3	Elementary Matrix		http://youtu.be/oQ2m6SSSquc
			3-4	Subspace		http://youtu.be/UTTUg6JUFQM
			3-5	Solutions Set		http://youtu.be/O0TPCpKW_eY
			3-6	Special Matrices		http://youtu.be/jLh77sZOaM8
			3-7	LU- Factorization		http://youtu.be/lKJPnLCiAVU
			3-8	Theorem of Triangular matrix		http://youtu.be/UriXEI-xoRk
4	?�?�식		4-1	Determinant		http://youtu.be/Vf8LlkKKHgg http://youtu.be/_3WRlwDUU9Y
			4-2	Cofactor Expansion		http://youtu.be/m6l2my6pSwY
			4-3	Cramer's Law		http://youtu.be/m2NkOX7gE50
			4-4	Appl of Determinant		http://youtu.be/KtkOH5M3_Lc
			4-5	Eigenvalue & Eigenvector		http://youtu.be/96Brbkx1cQ4
5	?�?�모??/P>		5-1	Power Method		http://youtu.be/CLxjkZuNJXw
			5-2	Encryption		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
6	?�?�변?�		6-1	Linear Transformation		http://youtu.be/Yr23NRSpSoM
			6-2	Linear Operator		http://youtu.be/12WP-cb6Ymc
			6-3	Kernel		http://youtu.be/H-P4lDgruCc
			6-4	Composite and Inverse		http://youtu.be/qfAmNsdlPxc
			6-5	Computer Graphic		http://youtu.be/VV5zzeYipZs
7	차원�?부분공�?		7-1	Basis Dimension		http://youtu.be/172stJmormk
			7-2	Fundamental Subspaces		http://youtu.be/dWoq2YVsy-g
			7-3	Rank Nullity Theorem		http://youtu.be/8P7cd-Eh328 http://youtu.be/bM-Pze0suqo
				Proof of Rank-Nullity Theorem		http://youtu.be/f3P4gfDVd8M
			7-4	Rank Theorem		http://youtu.be/BKZwJiuEYZE
			7-5	Projection Theorem		http://youtu.be/Rv1rd3u-oYg
				Proof of Schur Theorem		http://youtu.be/lL0VdTStJDM
			7-7	Gram-Schmidt ON Process		http://youtu.be/EBCi1nR7EuE
			7-9	Coordinate vectors		http://youtu.be/tdd7gbtCCRg
8	?�?�의 ?�각?�		8-1	Matrix of LT		http://youtu.be/jfMcPoso6g4
			8-2	similarity		http://youtu.be/MnfLcBZsV-I
			8-3	OrthoDiag		http://youtu.be/B—ABwoKAN4
			8-4	Quadratic Ft		http://youtu.be/lznsULrqJ_0
			8-5	Appl of Quadratic Function		http://youtu.be/cOW9qT64e0g
			8-6	Singular Value Decomposition		http://youtu.be/7-qG-A8nXmo
			8-7	Complex matrix		http://youtu.be/Ma2er-9LC_g
			8-8	Hermitian matrix		http://youtu.be/GLGwj6tzd60
9	?��?벡터공간		9-1	Vector Spaces		http://youtu.be/beXWYXYtAaI
			9-2	Inner product spaces		http://youtu.be/nIkYF-uvFdA
			9-3	Isomorphism		http://youtu.be/Y2lhCID0XS8
10	Jordan ?�준?� (with Sage)		10-1	Jordan Canonical Form		http://youtu.be/NBLZPcWRHYI
			10-3	Jordan Canonical Form with Sage		http://youtu.be/LxY6RcNTEE0

강?� 중 ?�?� 문제 ?�????발?� ?��?(?�?�?�)

???�료

201?�?� ?��?/SPAN>
강좌명		?�?�?�?�?�		?�당�??�		?�상�?/SPAN>
주차	?��?/SPAN>		section		?�?�?� 발?� ?�료
1주차	Inner product,Orientation		Section 1-1		http://youtu.be/fbCMyh-iDCQ
			Section 1-2		http://youtu.be/sEFj_7t_bqc
2주차	Vector (�???		Section 1-3		http://youtu.be/avVJfeEoeVs
			Chapter 1 (Discuss)		http://youtu.be/tys3taO5IHs
			Section 2-1		http://youtu.be/N5ltl-bfdvkz
			Section 2-2		http://youtu.be/sJeomjbRFmE
3주차	LSE		Section 2-3		http://youtu.be/vx_6rTJq5jk
			Section 3-1		http://youtu.be/LaAAruKbGyc
			Section 3-2		http://youtu.be/-MPszmMNvLE
			Section 3-3		http://youtu.be/ceI80eXp6xU
4주차	Change of basis, Similar matrices		Section 3-4		http://youtu.be/s7jxVvVAel4
			Section 3-5		http://youtu.be/IygHFdWacds
			Section 3-6		http://youtu.be/rYBsPkeVhQ0
5주차	Determinat		Section 4-1		http://youtu.be/Fne4gaZtE_Q
			Section 4-3		http://youtu.be/Ygu4_7I4fGQ
6주차	Linear transformations and their matrix representation		Section 6-1		http://www.youtube.com/watch?v=yDUHr2LHBVs
7주차	CAS system		Section 6-3		http://youtu.be/7BF0JG7JMJ8
			Section 6-4		http://youtu.be/qppP5y8bBgE
			Section 6-5		http://youtu.be/QoEPmoIZVd8
9주차	Dimension and Subspaces		Section 7-1		http://www.youtube.com/watch?v=BHf1AZjYAdQ
			Section 7-2
10주차			Section 7-3
			Section 7-4
			Section 7-5		http://www.youtube.com/watch?v=BC9qeR0JWis
			Section 7-6
11주차	Review Orthogonal and orthonormal bases and the Gram-Schmidt process		Section 7-7		http://youtu.be/ZRa-4MnWb48
			Section 7-9		http://youtu.be/X9VR_0Xnbcc
12주차	Diagonalization		Section 8-1		http://youtu.be/Oy7ZbacWDhk
	Orthogonal matrices, orthogonal similarity		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
13주차	orthogonal diagonalisability		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
14주차	Quadratic forms, Positive definite quadratic forms.		Section 8-9		http://www.youtube.com/watch?v=c0y5DcNQ8gs
	General Vector Spaces		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
15주차	Inner product spaces. Jacobian matrix. Hessian matrix Fourier series		Section 10-1		http://youtu.be/9-G3Fd2xOW0
			Chapter 10		http://www.youtube.com/watch?v=adWzUKKmO2k
16주차	Chapter 7,8,9 Project Presentation and Final Exam		Project 발?�		http://youtu.be/cxdj7hDWk08

http://matrix.skku.ac.kr/LinearAlgebra.htm