Timeline for About reducing the rank of a matrix by substract a diagonal matrix

10 events

when toggle format	what		by	license	comment
Dec 29, 2017 at 5:54	history	edited	YCor		edited tags
Dec 29, 2017 at 4:42	vote	accept	Minji Kim
Dec 29, 2017 at 3:49	history	edited	Minji Kim	CC BY-SA 3.0	edited tags; edited title
Dec 28, 2017 at 9:31	answer	added	Aaron Meyerowitz		timeline score: 3
Dec 28, 2017 at 4:16	comment	added	Gerry Myerson		OK, that's an example where you can reduce the rank by more than 1 (a simpler example would be $$\pmatrix{1&0&0\cr0&2&0\cr0&0&3\cr}$$ but what about in general?
Dec 28, 2017 at 2:28	comment	added	Minji Kim		1) For example, think of the matrix $\begin{bmatrix} 2 &2& 1\\ 2 & 6 & 2\\1 & 2 & 4\end{bmatrix}$. We cannot reduce its rank more than one by just substracting $\lambda I$, but if we substract $\begin{bmatrix} 1 &0& 0\\ 0 & 2 & 0\\0 & 0 & 3\end{bmatrix}$, we can reduce the rank by 2. 2) Yes, but I am especially interested in the case where $Q$ is positive definite.
Dec 27, 2017 at 19:45	answer	added	Alexandre Eremenko		timeline score: 4
Dec 27, 2017 at 16:05	comment	added	Gerry Myerson		Good question. But, 1) is there any reason to think that, in general, you can reduce the rank by more than 1? 2) why the restriction to positive definite matrices? isn't the question of interest for all matrices?
Dec 27, 2017 at 12:36	review	First posts
Dec 27, 2017 at 12:38
Dec 27, 2017 at 12:34	history	asked	Minji Kim	CC BY-SA 3.0