query: Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
positive_passages.docid: 146978
positive_passages.text: Minimal and characteristic polynomial have same set of irreducible factors
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 7833
negative_passages.text: Ideal and minimal polynomial
negative_passages.docid: 65305
negative_passages.text: Minimal polynomial for an invertible matrix and its determinant
negative_passages.docid: 53840
negative_passages.text: Understanding proof of unique factorization of polynomial in Linear Algebra Done Right
negative_passages.docid: 447
negative_passages.text: Minimal polynomial for T is a product of distinct linear factors
negative_passages.docid: 12166
negative_passages.text: How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
negative_passages.docid: 80188
negative_passages.text: There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field
negative_passages.docid: 14111
negative_passages.text: Determining possible minimal polynomials for a rank one linear operator
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 21853
negative_passages.text: When are minimal and characteristic polynomials the same?
negative_passages.docid: 149364
negative_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 63587
negative_passages.text: Possible Jordan Canonical Forms Given Minimal Polynomial
negative_passages.docid: 31215
negative_passages.text: Irreducible cyclotomic polynomial
negative_passages.docid: 114762
negative_passages.text: Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible.
negative_passages.docid: 134442
negative_passages.text: Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?