User smilingbuddha - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T12:57:50Z http://mathoverflow.net/feeds/user/12349 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118225/how-to-show-a-certain-determinant-is-non-zero How to show a certain determinant is non-zero smilingbuddha 2013-01-06T21:28:50Z 2013-03-28T18:34:16Z <p>For any $n$ distinct points $x_1,x_2 , \ldots , x_n$ on the real line show that the matrix $M$ where $M(i,j) = e^{\lambda_j x_i}$ has non-zero determinant where $\lambda_1 \lt \lambda_2 \lt \ldots \lt \lambda_n \in \mathbb{R}$ are fixed constants. </p> <p>I am able to show this for $n=1$(duh...) and $n=2$. Is this an inductive proof? </p> http://mathoverflow.net/questions/57060/convexity-and-line-segments Convexity and line segments smilingbuddha 2011-03-02T00:33:02Z 2011-03-02T00:33:02Z <p>Let S be a subset of a linear space. Let S1 be the union of all line segments that join pairs of points in S. Now what happens if we repeat this process and construct S2, S3,....(Thus for example S2 is the union of line segments in S1)?</p> <p>My guess is that the end-result should be the convex hull of the set S, but I am not able to prove/disprove this. </p> <p>Thank you,</p> <p>Sanjeev</p> http://mathoverflow.net/questions/57060/convexity-and-line-segments Comment by smilingbuddha smilingbuddha 2011-03-02T00:58:52Z 2011-03-02T00:58:52Z Ohhh yes indeed!! I guess that settles it....One question though... Does this constructed chain S1, S2, S3,... have to be infinite to become the convex hull? In R^2 it seems to me that S2 of any set becomes the convex hull.