Timeline for When do the eigenvectors of a $n\times n$ matrix span $\mathbb{R}^n$? (aka when is a matrix diagonalizable?)

6 events

when toggle format	what		by	license	comment
Nov 10, 2015 at 21:58	comment	added	Bernard		Yes, it should have only simple roots. But the characteristic polynomial can have roots with order of multiplicity $>1$.
Nov 10, 2015 at 21:55	comment	added	Andy Miles		@Bernard, just read about the Minimal Polynomial. You say "...splits as a product of distinct linear factors", does that mean that the minimal polynomial must not contain the same factor twice?
Nov 10, 2015 at 19:03	history	edited	Bernard	CC BY-SA 3.0	added 446 characters in body
Nov 10, 2015 at 18:47	comment	added	Alex Fish		Terrible answer! If he knew what a minimal polynomial is he would never ask that question in the first place. At least give some links or explanations. Even though it is the most correct answer as it is the only necessary and sufficient condition to my knowledge.
Nov 10, 2015 at 18:42	history	edited	Bernard	CC BY-SA 3.0	edited body
Nov 10, 2015 at 18:27	history	answered	Bernard	CC BY-SA 3.0