Linear Algebra (? ????) by SGLee

???λͺ¨λΈλ?: http://matrix.skku.ac.kr/2013-Album/2013-MM-Syllubus.htm

[New] ? ???? Interactive ??΅μ?(GeoGebra+Sage+κ°?λ‘+???)

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 Syllabus κ΅κ³Όλͺ©λͺ ? ???? ??λ²??/SPAN> GEDB003-42 ?¬μ©μΈμ?/SPAN> English ??­κ΅¬λ? κ΅?.κΈ°μ? ?κ°???λΆ all ?΄μκ΅¬λ? κ΅?.κΈ°μ? ??/?κ° 3?? / 3?κ° ?Έμ?κ΅¬λ? ??/?κΈ?/SPAN> 201*/* ?κΈ?/P> κ°???/SPAN> κΈ°μ??λ¬Έκ? 1μΈ?017?51155? ???κ° ?,λͺ?10:30~11:45 ?΄λΉκ?? λͺ ?΄μκ΅?κ΅? ?°λ½μ?(?°κ΅¬?? 031-290-7025 E-Mail sglee@skku.edu κ΅κ³Όλͺ© κ°? 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 κ΅κ³Όλͺ© λͺ©ν 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 (??? κ°?)

??Made by Prof. SGLee at Sungkyunkwan Univ.

 SKKU Linear Algebra with Sage κ°μ’λͺ ? ???? ?΄λΉκ?? sglee@skku.edu Ch. μ£Όμ  section ?΄μ?/SPAN> ??? κ°??λ£ 0 Preface http://youtu.be/CbfJYPCkbm8 Introduction  of CAS http://youtu.be/0SQpiNe2LU8 1 λ²‘ν?/P> 1-1 Vector http://youtu.be/85kGK6bJLns 1-2 Norm http://youtu.be/g55dfkmlTHE 1-3 Vector Equations http://youtu.be/YB976T1w0kE 2 ? ??°λ¦½λ°©μ ? 2-1 LSE http://youtu.be/AAUQvdjQ-qk 2-2 RREF 2-3 Appl of LSE http://youtu.be/G790BLDSK5g 3 ??¬κ³Ό ??¬λ? 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 ??¬μ 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 ??¬λͺ¨??/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 ? ?λ³? 6-1 Linear Transformation http://youtu.be/Yr23NRSpSoM 6-2 Linear Operator http://youtu.be/12WP-cb6Ymc 6-3 Kernel 6-4 Composite  and Inverse http://youtu.be/qfAmNsdlPxc 6-5 Computer Graphic http://youtu.be/VV5zzeYipZs 7 μ°¨μκ³?λΆλΆκ³΅κ? 7-1 Basis Dimension 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 ??¬μ ?κ°? 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 8-6 Singular Value Decomposition 8-7 Complex matrix http://youtu.be/Ma2er-9LC_g 8-8 Hermitian matrix http://youtu.be/GLGwj6tzd60 9 ?Όλ?λ²‘ν°κ³΅κ° 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 ?μ€? (with Sage) 10-1 Jordan Canonical Form http://youtu.be/NBLZPcWRHYI 10-3 Jordan Canonical Form with Sage http://youtu.be/LxY6RcNTEE0

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