het A be an man matrise. Prove that AA is (Orthogonally diagonalizable
Let A be an m*n matrix. Prove that AA(transpose) 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.
Indicate whether the statements are true or false (a) If A is orthogonally diagonalizable, then so is A2 (b) For any matrix A e Rmxn, AAT and AT A are symmetric matrices
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.
Suppose that A is diagonalizable and all eigenvalues of A are
positive real numbers. Prove that det (A) > 0.
(1 point) Suppose that A is diagonalizable and all eigenvalues of A are positive real numbers. Prove that det(A) > 0. Proof: , where the diagonal entries of the diagonal matrix D are Because A is diagonalizable, there is an invertible matrix P such that eigenvalues 11, 12,...,n of A. Since = det(A), and 11 > 0,..., n > 0,...
Prove or disprove
(8) Let T: V → V be linear. If T is diagonalizable, then T is invertible.
het T:V W be an isomorphism. Prove That ir & w, wg... ... on} is Set in wel, then the premages of dwe, log... an} a linearly Independent set knearly Independent 19
1. Let f : L→ L be a diagonalizable operator with a simple spectrum. a) Prove that any operator g L L such that 9f fg can be represented in -fg can be represented in the form of a polynomial of f. b) Prove that the dimension of the space of such operators g equals dim L. Are these assertions true if the spectrum of f is not simple?
1. Let f : L→ L be a diagonalizable operator with...
het ī: V W be an isomorphism. Prove That ir & w, wg yung is a is a linearly Set in wl, then the premages of dog. linearly Independent set in v nearly Independent ...., bo} 19