# Consider if then with an integer to obtain the

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: en is formed. Example. Find the logarithm of The roots of the characteristic equation give . Then recalling Euler’s formula, components of and Write to find and and solve for the . The transformation matrices are .■ . Finally Example. Find the logarithm of and, . Since is upper triangular, the eigenvalues are on the main diagonal. has 1 eigenvalue, , with multiplicity The associated generalized eigenspace is all of The simplest choice for a basis is and . Then the transformation matrices are . We thus have . has a nilpotent part so we have another term in the logarithm to compute. Note . 16 Chapter 2 part B Let . Then . According to [4] .■ Recall that we are trying to characterize the solutions of the initial value problem for a periodic linear system [2]. The fundamental matrix solution is the solution of the matrix initial value problem [3]. Any solution of [2] can be written The monodromy matrix is the solution of [3], with , after one period: Theorem 2.13 (Floquet). Let be the monodromy matrix for a -periodi...
View Full Document

## This document was uploaded on 02/24/2014 for the course MATH 512 at Washington State University .

Ask a homework question - tutors are online