Consider if then with an integer to obtain the

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

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