Timeline for Approximating a subspace by sampling a base without replacement
Current License: CC BY-SA 3.0
4 events
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| Jan 8, 2013 at 14:38 | comment | added | gappy3000 | See clarification to the question. The matrix is given. | |
| Jan 8, 2013 at 5:09 | comment | added | vxf | So now I think I get the bunbury comment. If we assume that we start with a fixed subspace S and then choose a random sequence of new vectors from the space X (in other words, the matrix is going to be generated at random) and ask for the distribution of angles between these new vectors and S then this is equivalent to choosing a random sequence of unit vectors in X. To answer that, we only have to compute the distribution for a single vector in X. Isn't this the same as putting a hyperplane through the origin of a sphere? | |
| Jan 8, 2013 at 4:52 | comment | added | vxf | I see now that you can not mean to measure the distance between the whole subspace and the sample subspace because that distance is going to be zero as a previous comment has mentioned. Instead, you are looking at the distance between each vector and the whole subspace. However, this depends heavily on the matrix as I mentioned. If the columns in the matrix are orthogonal, then the angles between the vectors and the subspace are either 0 or pi/2. | |
| Jan 8, 2013 at 4:15 | history | answered | vxf | CC BY-SA 3.0 |