Bounds for the Singular Values of a Matrix

A lower-bound theorem is developed for the singular values ofa matrix A (and therefore for the eigenvalues of B = A^HA). Itis found that there is always a unique column scaling of A whichproduces the optimum bound. However, sharper bounds still maysometimes be obtained by taking advantage of matrix partitioning.It is shown that the resulting bounds may often (but not always)be better than those obtained by applying Gerschgorin's theoremto B. The equivalent upper-bound theorem is found to be weak.