Counterexample

Is this true?

Two matrices with the same characteristic and minimal polynomials are similar

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Base field or ring

The answer changes with the field or ring you are working over.

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Rational canonical form and invariant factors· From Eigenvalues and Canonical Forms › Rational canonical form

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