*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **1 e 1 t v 21 + c 2 e 2 t v 22 : In order to determine the eigenvalues of a matrix A , set det( I A ) = 0, where I is the identity matrix, and solve for . For each eigenvalue , the corresponding eigenvectors are the nonzero solutions v of the matrix equation ( I A ) v = 0. If the 2 2 matrix A has repeated eigenvalues 1 = 2 = with only one independent eigenvector v , then one solution is given by x = e t v . The determination of a second, inde-pendent solution is beyond the scope of this course. If the 2 2 matrix A has complex eigenvalues, then x 1 = e 1 t v 1 and x 2 = e 2 t v 2 are two complex solutions. The extraction of two, real, independent solutions from the complex ones is beyond the scope of this course....

View
Full
Document