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 matrix.
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.