Where the minimal polynomial is identical to the characteristic polynomial, the Frobenius normal form is the companion matrix of the characteristic polynomial.
22.
There is a unique monic polynomial of minimal degree which annihilates " A "; this polynomial is the minimal polynomial.
23.
Any polynomial which annihilates " A " ( such as the characteristic polynomial ) is a multiple of the minimal polynomial.
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*PM : examples of minimal polynomials, id = 9184 new !-- WP guess : examples of minimal polynomials-- Status:
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*PM : examples of minimal polynomials, id = 9184 new !-- WP guess : examples of minimal polynomials-- Status:
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*PM : existence of the minimal polynomial, id = 4723-- WP guess : existence of the minimal polynomial-- Status:
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*PM : existence of the minimal polynomial, id = 4723-- WP guess : existence of the minimal polynomial-- Status:
28.
If \ varphi is not injective, let " p " ( X ) be a generator of its minimal polynomial of ?.
29.
This statement is equivalent to saying that the minimal polynomial of " A " divides the characteristic polynomial of " A ".
30.
Similarly ( 6, 15, 40 ) gives a matrix of which also has rank 3 when the degree of the minimal polynomial is 4.
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