English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this document I recapitulate some results by Hiriart-Urruty and Ye (1995)concerning the properties of differentiability and the existence of lateraldirectional derivatives of the multiple eigenvalues of a complex Hermitianmatrix function of several real variables, where the eigenvalues are supposedin a decreasing order. Another version of these results was obtained byJi-guang Sun (1988).  This 2020 version has been written following a remark raised by MiloudSadkane about the presence or not of the value 1/2 in the formulas that givethe lateral directional derivatives of multiple singular values. Therefore, Ihave added Theorem 9. I have also written in more detail the relationship ofthe reviewed results with those in the bibliography. Finally, I have also put aresult of mine (Corollary 11 in [1]) (joint with Armentia and Velasco) whichinterprets a Lippert's Theorem (2005).

Directional derivatives of the singular values of matrices depending on several real parameters