query: Characteristic polynomial divides minimal polynomial if and only if all eigenspaces are one-dimensional
positive_passages.docid: 21853
positive_passages.text: When are minimal and characteristic polynomials the same?
negative_passages.docid: 75536
negative_passages.text: every eigenvalue of $T$ has only one corresponding eigenvector up to a scalar multiplication
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 66714
negative_passages.text: Characteristic polynomial of companion matrix
negative_passages.docid: 149364
negative_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 18036
negative_passages.text: Localization by a non-nilpotent as a polynomial quotient
negative_passages.docid: 14111
negative_passages.text: Determining possible minimal polynomials for a rank one linear operator
negative_passages.docid: 57930
negative_passages.text: Chromatic polynomial properties
negative_passages.docid: 146046
negative_passages.text: Are two matrices having the same characteristic and minimal polynomial always similar?
negative_passages.docid: 119452
negative_passages.text: Nilpotent matrices with same minimal polynomial and nullity
negative_passages.docid: 116820
negative_passages.text: If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 75349
negative_passages.text: Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
negative_passages.docid: 146978
negative_passages.text: Minimal and characteristic polynomial have same set of irreducible factors
negative_passages.docid: 21578
negative_passages.text: Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
negative_passages.docid: 19280
negative_passages.text: Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond
negative_passages.docid: 54875
negative_passages.text: How to prove polynomials with degree $n$ does not form a vector space?