Timeline for the number of connected components
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2014 at 9:41 | comment | added | Sasha Anan'in | When you have a linear subspace $S$ of dimension $n$ such that $As=ds$ for all $s\in S$, the multiplicity of the eigenvalue $d$ of $A$ is at least $n$. This is elementary linear algebra. (To see this, you may write everything in the basis containing a basis of $S$.) | |
| Jan 20, 2014 at 9:28 | comment | added | user45655 | why multiplicity at least the number of connected components? | |
| Jan 20, 2014 at 9:17 | comment | added | Sasha Anan'in | The coefficients of the vector (= column) $[C]$ correspond to all the vertices $v$ of the graph $G$. By definition, $S$ is the the linear subspace of columns generated by all $[C]$'s. | |
| Jan 20, 2014 at 7:04 | comment | added | user45655 | v vertex or edge? S means that? | |
| Jan 17, 2014 at 11:46 | history | answered | Sasha Anan'in | CC BY-SA 3.0 |