query: Minimal polynomial is invariant under field extensions
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: 117970
negative_passages.text: Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$
negative_passages.docid: 65305
negative_passages.text: Minimal polynomial for an invertible matrix and its determinant
negative_passages.docid: 139499
negative_passages.text: The algebraic closure of a finite field and its Galois group
negative_passages.docid: 78561
negative_passages.text: Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 155828
negative_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
negative_passages.docid: 93062
negative_passages.text: Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?
negative_passages.docid: 7833
negative_passages.text: Ideal and minimal polynomial
negative_passages.docid: 68753
negative_passages.text: Elements in finite field extensions
negative_passages.docid: 11566
negative_passages.text: Similar matrices and minimal polynomial
negative_passages.docid: 63587
negative_passages.text: Possible Jordan Canonical Forms Given Minimal Polynomial
negative_passages.docid: 120940
negative_passages.text: An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
negative_passages.docid: 58490
negative_passages.text: Polynomials, finite fields and cardinality/dimension considerations
negative_passages.docid: 111347
negative_passages.text: Finding an example of field extensions satisfying certain properties
negative_passages.docid: 447
negative_passages.text: Minimal polynomial for T is a product of distinct linear factors