Let K be a field and A Mat n K. (a) 0 is an eigenvalue of
Question:
Let K be a field and A ϵ MatnK.
(a) 0 is an eigenvalue of A if and only if A is not invertible.
(b) If k1, ... , kr ϵ K are the (not necessarily distinct) eigenvalues of A and ∫ ϵ K[x], then ∫(A) ϵ MatnK has eigenvalues ∫(k1), ... ,∫(kr).
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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