Eigen Values

1. Eigen Values Andras Zakupszki Nuttapon Pichetpongsa Inderjeet Singh SuratWanamkang

2. Introduction • Team Structure & Roles • What is eigenvalues? • 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) • InderjeetSingh (Programmer) • SuratWanamkang(Researcher)

4. Introduction to Eigenvalues 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)

5. Eigen Values in Matlab eig Examples: d = eig(A) [V, D] = eig(A) Description: • d = eig(A) returns a vector of the eigenvalues of matrix A. • [V,D] = eig(A) produces matrices of eigenvalues (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

7. 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 generalize eigenvalue problem • Ax = λBx

10. The Task • Linear Equations • Quadratic Equations • Polynomial • Homogeneous Equations

11. Conclusion

12. References • http://www.mathworks.com/help/techdoc/ref/eig.html • http://www.swarthmore.edu/NatSci/echeeve1/Ref/MtrxVibe/EigMat/MatrixEigen.html • (http://www.numbertheory.org/, Keith Matthews, Australia)

13. Thank You !!!