Timeline for Probabilistic statement on matrix ranks

9 events

when toggle format	what		by	license	comment
Feb 10, 2015 at 11:57	comment	added	Turbo		Is there a way to quantify number of matrices which do not fit pattern?
Feb 4, 2015 at 16:28	comment	added	Jan-Christoph Schlage-Puchta		For all $r$ in the range given we have $\frac{rn}{2\log_2 n}>\frac{r^{\log_2^c r}}{2\log_2 r}$, so almost all rank $r$-matrices with entries in $\{0,1\}$ satisfy $1'_nA1_n >\frac{rn}{2\log_2 n}>\frac{r^{\log_2^c r}}{2\log_2 r}$.
Jan 30, 2015 at 2:34	vote	accept	Turbo
Jan 30, 2015 at 2:34	vote	accept	Turbo
Jan 30, 2015 at 2:34
Jan 30, 2015 at 2:34	vote	accept	Turbo
Jan 30, 2015 at 2:34
Jan 30, 2015 at 2:34	vote	accept	Turbo
Jan 30, 2015 at 2:34
Jan 30, 2015 at 2:34	vote	accept	Turbo
Jan 30, 2015 at 2:34
Jan 29, 2015 at 20:01	comment	added	Turbo		You are saying that: $$\forall r>0,c>0\exists n\in \Bbb N, A\in\{0,1\}^{n\times n}\mbox{ with }rank(A)=r: \frac{n}{2\log_2n}\ll\frac{r^{({\log_2r})^c}}{2\log_2r}?$$ This gives: $$1_n'A1_n<\frac{rn}{2\log_2n}\ll\frac{(r-1)r^{({\log_2r})^c}}{2\log_2r}?$$
Jan 29, 2015 at 17:46	history	answered	Jan-Christoph Schlage-Puchta	CC BY-SA 3.0