Let AA be an m×nm×n matrix. Prove that AATAAT is orthogonally diagonalizable.
Let AA be an m×nm×n matrix. Prove that AATAAT is orthogonally diagonalizable.
mathematics or linear algebra. Let AA be an m×nm×n matrix. Prove that AATAAT is orthogonally diagonalizable.
Let A be an m*n matrix. Prove that AA(transpose) is orthogonally diagonalizable.
het A be an man matrise. Prove that AA is (Orthogonally diagonalizable
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
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
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 = 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].45 -253 -378 A6 = 126 188 11
Let AA be an n×nn×n matrix. Prove that if x⃗ x→ is an eigenvector of AA corresponding to the eigenvalue λλ, then x⃗ x→ is also an eigenvector of A+cIA+cI, where cc is a scalar. Moreover, find the corresponding eigenvalue of A+cIA+cI.
is diagonalizable if 2. Let A be an nxn matrix and B be an m xm matrix. Show that and only if both A and B are diagonalizable.
Consider the matrix A=[acbd]. Assume that (a−d)2=−4bc(a−d)2=−4bc holds. Is AA always diagonalizable? If your answer is yes prove it. If your answer is no, give an example that shows AA is diagonalizable and give another example that shows AA is not diagonalizable.