Some aspects of Olga Taussky's work in algebra
In this article, Laffey mentions some of the myriad results obtained by Olga Taussky. In particular, he mentions her 1937 result on the structure of \(2\)-groups with commutator subgroup of index \(4\) and the applications to class field towers [J. Lond. Math. Soc. 1, 82-85 (1937; Zbl 0016.20002)]. The remarkable result with \textit{T. S. Motzkin} that if \(A\) and \(B\) are complex matrices such that \(xA+yB\) is diagonalizable for all \(x,y\) implies that \(A\) and \(B\) are simultaneously diagonalizable is also discussed [Trans. Am. Math. Soc. 80, 387-401 (1955; Zbl 0067.25401)]. Other results mentioned include the irreducibility of the variety of commuting pairs (also joint with Motzkin), the \(L\)-property (the property that the eigenvalues of \(xA+yB\) are of the form \(xa+yb\) where \(a\) and \(b\) are eigenvalues of \(A\) and \(B\), respectively) and trace forms. Laffey indicates the importance of these results and Taussky's uncanny knack for considering important concepts before they were known to be important. This short note sheds some interesting light on a small portion of Taussky's work.
scientific article; zbMATH DE number 1355310
scientific article