Timeline for A specific spanning property of a family of vectors
Current License: CC BY-SA 3.0
4 events
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| Aug 1, 2016 at 16:27 | comment | added | Fabian Wirth | @Fiego24: Well, now we need at least $3n$ vectors. In principle, what I have done is called taking the Schur complement. The Schur complement in the first display is the expression $V_2 A_2 - V_1 A_1V_1^{-1}V_2$. This you can do indefinitely, i.e., first make the $V,VA$ block full rank, permute so that the first $2n$ vectors are linearly independent, then take the next Schur complement etc. It is just that the formulas do not get prettier and the nice reduction to a Sylvester like equation seems to go away. At least I cannot see it offhand. | |
| Aug 1, 2016 at 15:29 | history | edited | Fabian Wirth | CC BY-SA 3.0 |
corrected a stupid mistake concerning the number $N$.
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| Aug 1, 2016 at 15:18 | comment | added | Fiego24 | oh this is great! I will read through it in detail soon. Do you have an idea how one can generalize this to higher-dimensional cases, i.e. $\begin{pmatrix} V \\ VA \\ VB \end{pmatrix}$ where $B$ is some other diagonal matrix? | |
| Jul 31, 2016 at 20:15 | history | answered | Fabian Wirth | CC BY-SA 3.0 |