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Shoe that two matrices have the same minimal polynomial

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Reference no: EM131587538

Question: (a) Show that if two matrices A, B ∈ Hn×n, n ≤ 3, have the same minimal polynomial, then they are similar.

(b) Show by example that the statement in (a) fails if n ≥ 4.

(a) Show that if two matrices A, B ∈ Hn×n, n ≤ 6, have the same minimal polynomial and the same geometric multiplicity for every eigenvalue, then they are similar.

(b) Show by example that the statement in (a) fails if n ≥ 7.

Reference no: EM131587538

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