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k 5. Find the matrix power (3 :) for k € N.
Write an algorithm that estimates the desired eigenvalues of an input matrix by using the power method. Your algorithm must find the i^th largest eigenvalues by using the power method and deflation to remove an already determined dominant eigenvalues. Save your algorithm as "LastnamePM.m." Your algorithm must be a function of A (input matrix), n (the number of iterations), and i (the i^th largest eigenvalues). For example, if you call "LastnamePM(A, 10,3)", the outcome will be the estimated 3,d largest...
Find the power of A for the matrix A = -1 0 0 0 - 1 0 0 0 0 OOOO OOOO 0 0 0 0 0 0 0 0 1 If A is the 2 x 2 matrix given by [aь A = cd and if ad - bc + 0, the inverse is given by d-b ad - bc Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an...
(1 point) Find a function of x that is equal to the power series En= n(n + 1)x" = for <x< Hint: Compare to the power series for the second derivative of 1-X (1 point) Find a formula for the sum of the series (n + 1)x" n=0 101+2 for –10 < x < 10. Hint: D,( *) = " " 10n+1
Suppose A is an n by n matrix that is diagonalized by P. Find a matrix that diagonalizes AT
Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = −4 0 4 −3 −1 4 −6 0 6 , A5
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = p-1AP is the diagonal form of A. Prove that A* = Pokp-1, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 18].46 A = 11
2. Discrete Fourier Transform.(/25) 1. N-th roots of unity are defined as solutions to the equation: w = 1. There are exactly N distinct N-th roots of unity. Let w be a primitive root of unity, for example w = exp(2 i/N). Show the following: N, if N divides m k=0 10, otherwise N -1 N wmk 2. Fix and integer N > 2. Let f = (f(0), ..., f(N − 1)) a vector (func- tion) f : [N] →...
Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B = P-1AP is the diagonal form of A. Prove that Ak = Pekp-1, where k is a positive integer. Use the result above to find the indicated power of A. 0-2 02-2 3 0 -3 ,45 A5 = 11
Find the characteristic polynomial of the matrix, using either a cofactor expansion or th 4 0 6 - 3 2 6 006 The characteristic polynomial is (Type an expression using 2 as the variable.)