edu.berkeley.cs.amplab.mlmatrix
Create several linear systems with varying condition numbers and thetas, where theta is the angle between the vector b and the range of A.
Create several linear systems with varying condition numbers and thetas, where theta is the angle between the vector b and the range of A. We create a matrix A with a specific condition number by first setting the entries of a diagonal matrix to be the desired singular values of A, and then hitting this diagonal matrix with orthogonal matrices U and V on the left and right respectively. When we create the matrix U, we create a matrix with one additional column, called qe. The vector qe is then orthogonal to the range of A and we can use qe to create a vector b at the specified angle theta away from the range of A.