The fundamental matrix solution is the solution of

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Unformatted text preview: c linear system and its logarithm. Then there exists a -periodic matrix such that the fundamental solution is . Proof. Give as in the text. Remark. Note that period the matrices ). and . This implies for an integer. Then . However, when is not an integer multiple of a may be complex (consider when is the square root of Alternatively there is a real form of Floquet’s theorem. It is based upon the fact that the square of any real matrix has a real logarithm (Exercise #21). Theorem 2.14. Let be the fundamental matrix solution for the time T-periodic linear system [2]. Then there exists a real -periodic matrix and a real matrix such that . Proof. From exercise 21, for any nonsingular matrix Define , and then there is a real matrix . Therefore, is -periodic. □ such that...
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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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