An algebraic proof of a result by Gonzaga and Lara (Q1964340)

In this note the authors present another proof to the equality of two condition numbers of a rectangular matrix introduced by \textit{G. W. Stewart} [ibid. 112, 189-193 (1989; Zbl 0658.15003)]. The proof is not simpler than the earlier proof of \textit{C. C. Gonzaga} and \textit{H. J. Lara} [ibid. 261, 269-273 (1997; Zbl 0881.15006)], but it exploits only purely algebraic means.