Hi rochfor1,
Now I understand that it's not right to compare null(D) and row(E), since they are of different dimensions.
Can we compare the projections to null(D) and row(E) in terms of their effects to the separability of the pairs of vectors, (c11 , c12) ... (cn1 , cn2) I mentioned in...
Thank you for your reply!
You are right, E and D are matrices. Let me state my question more clearly.
I want to find a projection that maximally preserves the Euclidean distance between two points (vectors in general). Consider a 2-D example as show in the figure. The direction that maximally...
Suppose I have 3 vectors e1, e2, e3 that spans the subspace E, another 3 vectors d1, d2, d3 that spans the subspace D. If I also know that e1’d1 = 0, e2’d2 = 0, e3’d3 = 0, are there any conclusions I can make in terms of E and D? like row(E) = null(D)?
about null space projection
Homework Statement
If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of...
Hello everyone,
If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of (x-y)’, denoted as row( (x-y)’...