matlab Diagonalization

matlab Diagonalization - Eigen Problems and Diagonalization...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Eigen Problems and Diagonalization Using Matlab An Eigenproblem for a given matrix A requires finding the set of vectors, x , and the scalar numbers λ such that A x = λ x . In other words, we want the vectors which, when operated on by A , are simply multiples of the orginal vector. Matlab allows for easy computation of the eigenvalues and eigenvectors of any square matrix. For example, consider the following Matlab commands: > A = [-3 1 -3; -8 3 -6; 2 -1 2] A =-3 1-3-8 3-6 2-1 2 To find the eigenvalues of A we could use the fact that the eigenvalues, λ satisfy the characteristic equation given by det ( A- λI ) = 0 . Matlab has an easy way of entering this. Simply use the poly command: > p = poly(A) p = 1-1 2 The result says that the characteristic polynomial is: p ( λ ) = λ 3- 2 λ 2- λ + 2 = 0 This can be factored into: ( λ- 1)( λ + 1)( λ- 2) Which gives us the eigenvalues of A directly. If you don’t see the factorization easily, Matlab is equipped to solve the characteristic equation for you using the roots() command, > eigs = roots(p) eigs = 2 1-1 which gives the zeros (eigenvalues) of the polynomial directly. Now we can solve for the eigenvectors of A . For each eigenvalue, we must solve ( A- λI ) x = 0 for the eigenvector x . In Matlab the n × n identity matrix is given by eye(n) . To find the eigenvector associated with λ = 2 we could use: 1 Eigen Problem Solution Using Matlab...
View Full Document

This note was uploaded on 01/16/2011 for the course MATH 216 taught by Professor Mckinley,s during the Fall '08 term at Duke.

Page1 / 5

matlab Diagonalization - Eigen Problems and Diagonalization...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online