query: Minimal polynomials for a matrice in a given field and in its extension
positive_passages.docid: 146715
positive_passages.text: A square matrix has the same minimal polynomial over its base field as it has over an extension field
negative_passages.docid: 46265
negative_passages.text: Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
negative_passages.docid: 447
negative_passages.text: Minimal polynomial for T is a product of distinct linear factors
negative_passages.docid: 57515
negative_passages.text: Similar matrices and field extensions
negative_passages.docid: 82295
negative_passages.text: Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
negative_passages.docid: 15811
negative_passages.text: Finding a basis for a certain vector space of periodic polynomials
negative_passages.docid: 33611
negative_passages.text: necessary and sufficient condition for trivial kernel of a matrix over a commutative ring
negative_passages.docid: 99756
negative_passages.text: Squarefree polynomials over finite fields
negative_passages.docid: 10585
negative_passages.text: Does a polynomial that's bounded below have a global minimum?
negative_passages.docid: 94256
negative_passages.text: Partial factorization of multivariate polynomials in terms of given polynomials
negative_passages.docid: 31606
negative_passages.text: Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
negative_passages.docid: 75349
negative_passages.text: Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 115541
negative_passages.text: Subrings of polynomial rings over the complex plane
negative_passages.docid: 31029
negative_passages.text: Characteristic polynomial of a matrix of $1$'s
negative_passages.docid: 21422
negative_passages.text: Multivariate polynomial with no mixed terms
negative_passages.docid: 89553
negative_passages.text: proof that every finite matrix has an annihilating polynomial