Is the following statement true? Same characteristic polynomial ⇒ similar

No. 0 matrix and [[0,1],[0,0]] Both have char poly x², different minimal polynomials (x vs x²).

Counterexample

Is this true?

Same characteristic polynomial ⇒ similar

No — it is false.

The counterexample

0 matrix and [[0,1],[0,0]]

Why it fails

Both have char poly $x^{2}$ , different minimal polynomials (x vs $x^{2})$ .

Keep practicing

Execution slip

The idea was right. The computation was not.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.