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Eigen Values
Andras ZakupszkiNuttapon Pichetpongsa
Inderjeet SinghSurat Wanamkang
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Introduction
• Team Structure & Roles• What are Eigen Values?• Eigen Values in Matlab• Example• Example (Matlab)• The Eigen Values Problem• Our Task• Conclusion • References
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Team Structure & Roles
• Andras Zakupszki (Team Leader & Researcher)
• Nuttapon Pichetpongsa (Programmer)
• Inderjeet Singh (Programmer)
• Surat Wanamkang (Researcher)
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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)
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Eigen Values in Matlabeig
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.
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Example
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Example
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Example (Matlab)
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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
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The Task
Linear Equations
Quadratic Equations
Polynomial
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Conclusion
• Introducing the topic
• The problem
• The product
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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)
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Thank You !!!