Timeline for Intersection of subspaces
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2015 at 20:06 | comment | added | Mateus Araújo | Note that the $^t$ in the Anderson-Duffin formula is not a transpose, but the Moore-Penrose pseudoinverse, usually denoted by $^+$. | |
| Sep 27, 2012 at 13:22 | comment | added | Igor Rivin | All these are good ideas, thanks (I had something along these lines implemented)! I guess elegance is in the eye of the beholder -- treating subspaces as projections seems to have a certain appeal... | |
| Sep 27, 2012 at 2:19 | comment | added | John Wiltshire-Gordon | Put one basis on top of the other and compute the nullspace by row reduction. This writes the intersection in both bases. | |
| Sep 26, 2012 at 23:07 | comment | added | Anthony Quas | Here is what I see as a more elegant method: Column(-echelon?) reduce the base matrices for the subspaces. Use these matrices to write the subspaces as kernels of a family of independent linear functionals (one for each non-principal row in the column reduction). Combine these matrices and row reduce. Deduce the kernel of the combined matrix, which is of course the intersection of the two subspaces. I haven't thought about the time... | |
| Sep 26, 2012 at 16:33 | history | edited | Igor Rivin | CC BY-SA 3.0 |
added a transpose
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| Sep 26, 2012 at 16:18 | history | edited | Igor Rivin | CC BY-SA 3.0 |
clarification
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| Sep 26, 2012 at 16:06 | comment | added | Will Sawin | 1. How fast is it to view the bases as the columns of two tall thin matrices, concatenate them horizontally, take the kernel, then look at the image of that subspace under the left matrix only? 2. As far as I can tell your method fails when $V_1$ and $V_2$ are disjoint but not orthogonal. | |
| Sep 26, 2012 at 15:59 | history | asked | Igor Rivin | CC BY-SA 3.0 |