# vxf

 1 Reputation 2 views

## Unregistered User

 Name vxf Member for 4 months Seen Jan 8 at 4:52 Website Location Age
 Jan8 comment Approximating a subspace by sampling a base without replacementSo 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? Jan8 comment Approximating a subspace by sampling a base without replacementI 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. Jan8 answered Approximating a subspace by sampling a base without replacement