Linear Algebra with Sage        
 

Chapter 1. Vectors

*1.1 Vectors in n-space n-dim. space

    1.2  Inner product and Orthogonality

     1.3 Vector equations of lines and planes

 

Chapter 2. Linear system of equations

2.1 Linear system of equations

2.2 Gaussian elimination and Gauss-Jordan elimination

Exercise

    Quiz :

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

Chapter 3. Matrix and Matrix Algebra

 

 3.1 Matrix operation

 3.2 Inverse matrix

 3.3 Elementary matrix

 3.4 Subsapce and linear independence

 3.5 Solution set of a linear system and matrix

 3.6 Special matrices

*3.7 LU-decomposition

 

Chapter 4. Determinant

4.1 Definition and Properties of the Determinants

4.2 Cofactor Expansion and Applications of the Determinants

4.3 Cramer's Rule

*4.4 Application of Determinant

4.5 Eigenvalues and Eigenvectors

 

*Chapter 5. Matrix Model

5.1 Lights out Game

5.2 Linear Model (Google)

5.3 Exam and Project

 

Chapter 6. Linear Transformations

6.1 Matrix as a Function (Transformation)

6.2 Geometric Meaning of Linear Transformations

6.3 Kernel and Range

6.4 Composition of Linear Transformations and Invertibility

6.5*Computer Graphics with Sage

Exercises

 

Chapter 7. Dimension and Subspaces

7.1 Properties of bases and dimensions

7.2 Basic spaces of matrix

7.3 Rank-Nullity theorem

7.4 Rank theorem

7.5 Projection theorem

*7.6 Lleast square solution

7.7 Gram-Schmidt orthonomalization process

7.8 QR-Decomposition; Householder transformations

7.9 Coordinate vectors

Exercises

Chapter 8. Diagonalization

8.1 Matrix Representation of LT

8.2 Similarity and Diagonalization

8.3 Diagonalization with orthogonal matrix, *Function of matrix

8.4 Quadratic forms

*8.5 Applications of Quadratic forms

8.6 SVD and generalized eigenvectors

8.7 Complex eigenvalues and eigenvectors

8.8 Hermitian, Unitary, Normal Matrices

*8.9 Linear system of differential equations

Exercises

 

Chapter 9. General vector spaces

 9.1 Vector spaces

 9.2 Inner product spaces

 9.3 Isomorphism

 

Chapter 10. Jordan Canonical Form

10.1 Finding the Jordan Canonical Form with a Dot Diagram

*10.2 Jordan Canonical Form and Generalized Eigenvectors

10.3 Jordan Canonical Form and CAS

Exercises

 

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
SOCW: 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/sglee/LADef/defin.htm (정의집)
http://matrix.skku.ac.kr/sage

http://sage.skku.edu
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

Main Author : Sang-Gu Lee

 

Co-Authors : ***

Made by Prof. Sang-Gu LEE(sglee at skku.edu)

Copyright at Sungkyunkwan University, March 2013