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Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values
WHAT ARE EIGEN VALUES?
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Are a special set of scalars
associated with a linear system of
equations (i.e., a matrix equation).
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values• They are sometimes also known as
• characteristic roots, characteristic values
(Hoffman and Kunze 1971)
• proper values, or latent roots (Marcus and Minc
1988, p. 144).
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values
HOW TO DETERMINE THE EIGEN VALUES?
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Letting A be a kxk square matrix
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•With eigenvalue , then the corresponding eigenvectors satisfy
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•With is equivalent to the homogenous system
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Equation can be written compactly as
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Where I is the identity matrix. As shown in Cramer’s rule, a linear system of equations has nontrivial solutions if the determinant vanishes, so the solutions of the equation is given by
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values
•This equation is known as the characteristic equation of A, and the left hand side is known as the characteristic polynomial.
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values
EXAMPLES?
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Find the eigenvalues of the given matrix
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Find the eigenvalues of the given matrix
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values•Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values• Solution:
Technological University of the Philippines – Advance Mathematics – Electronics Engineering
Eigen Values• Solution:
