Let A R n,n and let be the characteristic polynomial of A. 1. Assume A is
Question:
Let A ∈ Rn,n and let
be the characteristic polynomial of A.
1. Assume A is diagonalizable. Prove that A annihilates its own characteristic polynomial, that is
2. Prove that p(A) = 0 holds in general, i.e., also for non-diagonalizable square matrices.
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To address both parts of the question well start by clarifying some notations and concepts Given a matrix A Rnn its characteristic polynomial is defin...View the full answer
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ISBN: 9781107050877
1st Edition
Authors: Giuseppe C. Calafiore, Laurent El Ghaoui
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