1. Eigen Values Andras Zakupszki Nuttapon Pichetpongsa Inderjeet Singh Surat Wanamkang

2. Introduction Team Structure & Roles What are Eigen Values? Eigen Values in Matlab Example Example (Matlab) The Eigen Values Problem Our Task Conclusion References

3. Team Structure & Roles Andras Zakupszki (Team Leader & Researcher) Nuttapon Pichetpongsa (Programmer) Inderjeet Singh (Programmer) Surat Wanamkang (Researcher)

4. Introduction to Eigen Values and Eigenvectors Mathematical expression: “Let A be a complex square matrix. Then if λ is a complex number and X a non–zero complex column vector satisfying AX = λX, we call X an eigenvector of A, while λ is called an eigenvalue of A. We also say that X is an eigenvector corresponding to the eigenvalue λ.” (http://www.numbertheory.org/, Keith Matthews, Australia)http://www.numbertheory.org/

5. Eigen Values in Matlab eig Examples: d = eig(A) [V, D] = eig(A) Description: d = eig(A) returns a vector of the Eigen Value of matrix A. [V,D] = eig(A) produces matrices of Eigen Values (D) and eigenvectors (V) of matrix A, so that A*V = V*D. Matrix D is the canonical form of A — a diagonal matrix with A's eigenvalues on the main diagonal. Matrix V is the modal matrix — its columns are the eigenvectors of A.

6. Example

8. Example (Matlab)

9. The Eigen Values Problem Determine solution of equation AX=λX A=n-by-n matrix X=eigenvector λ=eigenvalue To solve λ and X More general problem with Eigen Values Ax = λBx

10. The Task  Linear Equations  Quadratic Equations  Polynomial

11. Conclusion Introducing the topic The problem The product

12. References  http://www.mathworks.com/help/techdoc/ref /eig.html http://www.mathworks.com/help/techdoc/ref /eig.html  http://www.swarthmore.edu/NatSci/echeeve 1/Ref/MtrxVibe/EigMat/MatrixEigen.html http://www.swarthmore.edu/NatSci/echeeve 1/Ref/MtrxVibe/EigMat/MatrixEigen.html  (http://www.numbertheory.org/, Keith Matthews, Australia)http://www.numbertheory.org/

13. Thank You !!!