Subspaces that Minimize the Condition Number of a Matrix
S. Joshi and S. Boyd
Rejecta Mathematica, 1(1):4-9, July 2009.
We define the condition number of a nonsingular matrix on a subspace, and consider the problem of finding a subspace of given dimension that minimizes the condition number of a given matrix. We give a general solution to this problem, and show in particular that when the given dimension is less than half the dimension of the matrix, a subspace can be found on which the condition number of the matrix is one.