Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Let A be a diagonalizable n × n matrix, and let p(λ) = det(A − λI) be the
characteristic polynomial of A. Let P be an invertible matrix such that P −1AP = D, where
D is the diagonal matrix whose diagonal entries are the eigenvalues of A. Show that trace(A) = trace(D). Then show that the trace of an n × n
diagonalizable matrix is the sum of the eigenvalues of that matrix.

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Step 2: Show that trace(A) = trac(D) and trace of an n × n diagonalizable matrix is the sum its eigenvalues
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