Eigen Values

Eigen Values

Andras ZakupszkiNuttapon Pichetpongsa

Inderjeet SinghSurat Wanamkang

Introduction

• Team Structure & Roles• What is eigenvalues?• Eigen Values in Matlab• Example• Example (Matlab)• The Eigen Values Problem• Our Task• Conclusion • References

Team Structure & Roles

• Andras Zakupszki (Team Leader & Researcher)

• Nuttapon Pichetpongsa (Programmer)

• Inderjeet Singh (Programmer)

• Surat Wanamkang (Researcher)

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)

Eigen Values in Matlabeig

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.

Example

Example

Example (Matlab)

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

The Task

Linear EquationsQuadratic EquationsPolynomialHomogeneous Equations

Conclusion

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)

Thank You !!!