A note on the Ostrowski-Schneider type inertia theorem in Euclidean Jordan algebras

作者：Tao Jiyuan^*

来源：Linear Algebra and Its Applications, 2011, 434(8): 1902-1909.

DOI：10.1016/j.laa.2010.11.048

• Cauchy matrix
• Euclidean Jordan algebras
• Ostrowski-Schneider theorem

In a recent paper [7], Gowda et al. extended Ostrowski-Schneider type inertia results to certain linear transformations on Euclidean Jordan algebras. In particular, they showed that In(a) = In(x) whenever a o x > 0 by the min-max theorem of Hirzebruch, where the inertia of an element x in a Euclidean Jordan algebra is defined by
In(x) : = (pi(x), nu(x), delta(x)),
with pi(x), nu(x), and delta(x) denoting, respectively, the number of positive, negative, and zero eigenvalues, counting multiplicities. In this paper, we present a Peirce decomposition version of Wimmer's result [13] and show that it is equivalent to the above result. In addition, we extend Higham and Cheng's result ([8], Lemma 4.2) to the setting of Euclidean Jordan algebras.

• 出版日期2011-4-15