Show that every eigenvalue of such a matrix is necessarily real. Let A be an n
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Show that every eigenvalue of such a matrix is necessarily real.
Let A be an n × n real matrix with the property that AT = A, let x be any vector in Cn, and let q = X̅T Ax. The equalities below show that q is a real number by verifying that q̅ = q. Give a reason for each step.
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q = x Ax = x¹Ax = x¹AX = (x¹Ax) = x¹A¹ x = q (a) (b) (c) (d) (e)
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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