Report Number: CS-TR-72-319
Institution: Stanford University, Department of Computer Science
Title: On a characterization of the best $\ell_2$ scaling of a
Author: Golub, Gene H.
Author: Varah, James M.
Date: October 1972
Abstract: This paper is concerned with best two-sided scaling of a
general square matrix, and in particular with a certain
characterization of that best scaling: namely that the first
and last singular vectors (on left and right) of the scaled
matrix have components of equal modulus. Necessity,
sufficiency, and its relation with other characterizations
are discussed. Then the problem of best scaling for
rectangular matrices is introducted and a conjecture made
regarding a possible best scaling. The conjecture is verified
for some special cases.