Timeline for Computing the intersection of dual affine subspaces
Current License: CC BY-SA 3.0
4 events
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| Aug 24, 2011 at 13:01 | history | edited | user17348 | CC BY-SA 3.0 |
added 68 characters in body
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| Aug 24, 2011 at 7:04 | comment | added | user17348 | Apologies. The first plane is a simple $k$ dimensional affine subspace of $R^d$ of the form $Ax=B$. The other plane is defined depending on the convex function $\phi$ , and is of the form $C \nabla y = D$, where $C$ is a $d−k$ by $d$ dimensional matrix, and $\nabla y$ represents the gradient vector induced by $\phi$ at point $y \in R^d$. This is clearly not an affine plane in the conventional sense and describes some sort of curved surface.However, in the "dual space" obtained by taking the Legendre transform of $(R^n, \phi)$, this will be an affine plane. | |
| Aug 24, 2011 at 0:52 | comment | added | Andreas Blass | Maybe this question is clear to the experts, but I could sure use some clarification. For example, what is meant by the intersection of two planes when one is "in the original space" and the other is "in the dual space"? And what does that have to do with $\phi$ and its Legendre transform? | |
| Aug 23, 2011 at 21:22 | history | asked | user17348 | CC BY-SA 3.0 |