The eigenvalues and eigenvectors for the cat map matrix C = 1 1 1 2 are 1 = 3 + 5 2 , 2
Chapter 10, Problem T2(choose chapter or problem)
The eigenvalues and eigenvectors for the cat map matrix C = 1 1 1 2 are 1 = 3 + 5 2 , 2 = 3 5 2 , v1 = 1 1 + 5 2 , v2 = 1 1 5 2 Using these eigenvalues and eigenvectors, we can define D = 3 + 5 2 0 0 3 5 2 and P = 1 1 1 + 5 2 1 5 2 and write C = PDP 1; hence, Cn = PDn P 1. Use a computer to show that Cn = c (n) 11 c (n) 12 c (n) 21 c (n) 22 where c (n) 11 = 1 + 5 2 5 3 5 2 n 1 5 2 5 3 + 5 2 n c (n) 22 = 1 + 5 2 5 3 + 5 2 n 1 5 2 5 3 5 2 n and c (n) 12 = c (n) 21 = 1 5 3 + 5 2 n 3 5 2 n3 How can you use these results and your conclusions in Exercise T1 to simplify the method for computing (p)?
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