MATH136 Lecture Notes - Diagonalizable Matrix, Diagonal Matrix
29 Apr 2014
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MATH136 Full Course Notes
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Friday, april 4 lecture 36 : diagonalizable matrices : applications. Concepts : apply the matrix diagonalization process in various problems. 36. 1 application of matrix diagonalization the given matrix a:was diagonalized previously. Solution: we found above the diagonalizing matrix x, x 1 and d. This example is a particular case of a more general statement: 36. 1. 1 proposition let a be diagonalizable matrix with diagonalizer p and diagonal matrix d = p 1ap. Then for any positive integer n, an = pdnp 1. 36. 2 an application of eigenvalues to a number theory question: Consider the special sequence of numbers 1, 1, 2, 3, 5, 8, 13, where each number is the sum of it"s two predecessors xk + 2 = xk + 1 + xk. The tools just developed on eigenvalues and eigenvectors allow us to do this. Let x0 = 1 and x1 = 1 be the first two terms of the fibonacci sequence (described above)
