Timeline for Geometric interpretation of matrix minors
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2011 at 9:21 | vote | accept | joel | ||
| Sep 17, 2011 at 20:27 | |||||
| Sep 13, 2011 at 9:21 | comment | added | joel | i think you've helped me quite much, so please excuse my overfamiliar and presumptuous behaviour—i hadn't in mind giving orders to anybody: i just don't feel the courtesy and politeness levels of the language good enough yet.<br>mind to explore the topic little further as you proposed? :) | |
| Sep 13, 2011 at 1:54 | comment | added | Qiaochu Yuan | @joel: I don't appreciate receiving a command like "tell me X." I think this is a purely geometric description, if one just starts with a suitably geometric intuition for the exterior algebra, so perhaps you should be asking about that instead. | |
| Sep 13, 2011 at 0:19 | comment | added | joel | can i say then that minor of 'codegree' 1 describes measure of parallelotope's face of codimension 1 spaned by appropriate vectors? if so, what can i say about other minors in similar manner—what are principal minors then? (i'm afraid that hodge duality might spring out… ;p) tell me how to interpret laplace formula where minors show up (i won't have problems with cofactors—signs seem to come from keeping track of orientation…) probably your answer is definite but i'm still looking here for purely geometrical description which i could understand—care to give completely new answer? :p | |
| Sep 12, 2011 at 21:16 | comment | added | Qiaochu Yuan | @joel: a wedge product $v_1 \wedge ... \wedge v_k$ describes an oriented $k$-paralleletope with vertices $0, v_i, v_i + v_j, ...$ and $T$ acts on it by sending it to the paralleletope described by $T(v_1) \wedge ... \wedge T(v_k)$. Writing this in terms of sums of exterior products of a fixed basis of $W$ corresponds to slicing up the paralleletope along various axes. | |
| Sep 12, 2011 at 21:06 | comment | added | joel | i just forgot about exterior algebra… :p i just don't get it thoroughly but as far as i get it: the question i posed in your language would sound like 'how does $T$ it act on those parallelotopes…?' could you dwell little bit more on this? i must confess i'd be more satisfied seeing more school geometry here—care to translate from exterior algebra? :p | |
| Sep 12, 2011 at 19:04 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |