I have any matrix A and add a row of only zeros except for one 1 in any position.
I have a little prior knowledge about A but nothing that seems very helpful in my eyes (very sparse, most nonzero-elements are either 1, -1 or a real value close to 1)
What can i say about the new singular values of the matrix? I am especially interested in the first and the last singular value.
Is there any hint where to place the 1 in the new row vector to minimize the condition without trying out all possible positions?
I also want to repeat this procedure for a few times, is there any relation to previously added rows?
Thanks in advance!