If A E F is a characteristic root of T then A is a root of the minimal polynomial of T. In particular, T only has a finite number of characteristic roots in F.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.6: Algebraic Extensions Of A Field
Problem 14E
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If A E F is a characteristic root of T then A
is a root of the minimal polynomial of T.
In particular, T only has a finite number of
characteristic roots in F.
Transcribed Image Text:If A E F is a characteristic root of T then A is a root of the minimal polynomial of T. In particular, T only has a finite number of characteristic roots in F.
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