Timeline for Does this simple inequality have a name?

9 events

when toggle format	what		by	license	comment
Sep 22, 2014 at 0:42	answer	added	M. Lin		timeline score: 2
Sep 17, 2014 at 21:04	comment	added	David Handelman		If $A$ has eigenvalues (counting multiple ones, including what are sometimes called algebraic ones, really bad terminology) $(x_i)$, then ${\rm tr}\ A = \sum x_i$ and ${\rm tr}\ A^2 = \sum x_i^2$.
Sep 17, 2014 at 15:00	comment	added	Felix Goldberg		@DavidHandelman Can you please elaborate a bit? 10x!
Sep 17, 2014 at 13:58	comment	added	David Handelman		If $A$ is an $n \times n$ matrix, this inequality describes a relationship between ${\rm tr}\ A$ and ${\rm tr}\ A^2$.
Sep 17, 2014 at 8:37	answer	added	gsa		timeline score: 5
Sep 17, 2014 at 8:26	history	edited	Felix Goldberg	CC BY-SA 3.0	edited title
Sep 17, 2014 at 8:23	comment	added	Felix Goldberg		@J.E.Pascoe That's a nice proof - thanks! Still looking for the provenance, though...
Sep 17, 2014 at 8:13	comment	added	J. E. Pascoe		I guess this is equivalent to the inequality $x^2 \leq x(m+M) - Mm,$ since it must be true term by term ($n=1$ case seems to imply the claim in general). So that inequality might have a name if such a thing exists. The fact that $M \geq x$ then immediately implies the claim, so it might not, because it could be seen as being too easy, since it doesn't seem like there's any trick.
Sep 17, 2014 at 7:53	history	asked	Felix Goldberg	CC BY-SA 3.0