query: Is the Converse of the Cayley-Hamilton Theorem true or not?
positive_passages.docid: 37764
positive_passages.text: Is the converse of Cayley-Hamilton Theorem true?
negative_passages.docid: 59531
negative_passages.text: Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
negative_passages.docid: 42334
negative_passages.text: Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
negative_passages.docid: 63559
negative_passages.text: Is there a more complete way of proving this theorem (that I devised)? OR does this theorem already exist and have a name?
negative_passages.docid: 18125
negative_passages.text: Counterexamples to the converse to Lagrange's Theorem different from $A_{4}$.
negative_passages.docid: 22424
negative_passages.text: Has this "generalized semidirect product" been studied?
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 110944
negative_passages.text: Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
negative_passages.docid: 4196
negative_passages.text: A valid proof for the invariance of domain theorem?
negative_passages.docid: 31252
negative_passages.text: "Efficient version" of Cayley's Theorem in Group Theory
negative_passages.docid: 80892
negative_passages.text: Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
negative_passages.docid: 113840
negative_passages.text: Does converse of Lagrange's theorem hold for a group of order 21?
negative_passages.docid: 54791
negative_passages.text: Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
negative_passages.docid: 26671
negative_passages.text: Does this seemingly elementary question require König's theorem?
negative_passages.docid: 49439
negative_passages.text: Matrix exponential via Cayley-Hamilton Theorem
negative_passages.docid: 120065
negative_passages.text: Niven’s theorem proof.
negative_passages.docid: 56446
negative_passages.text: A kind of converse of Lagrange's Theorem