On the Higher-Order Derivatives of Spectral Functions: Two Special Cases
| dc.creator | Sendov, Hristo S. | |
| dc.date | 2004-04-19 | |
| dc.date.accessioned | 2026-07-07T05:07:34Z | |
| dc.date.available | 2026-07-07T05:07:34Z | |
| dc.description | In this work we use the tensorial language developed in [8] and [9] to differentiate functions of eigenvalues of symmetric matrices. We describe the formulae for the k-th derivative of such functions in two cases. The first case concerns the derivatives of the composition of an arbitrary differentiable function with the eigenvalues at a matrix with distinct eigenvalues. The second development describes the derivatives of the composition of a separable symmetric function with the eigenvalues at an arbitrary symmetric matrix. In the concluding section we re-derive the formula for the Hessian of a general spectral function at an arbitrary point. Our approach leads to a shorter, streamlined derivation than the original in [6]. The language we use, based on the generalized Hadamard product, allows us to view the differentiation of spectral functions as a routine calculus-type procedure. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404349 | |
| dc.identifier | http://arxiv.org/abs/math/0404349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70906 | |
| dc.subject | Optimization and Control | |
| dc.subject | Spectral Theory | |
| dc.subject | primary: 49R50; 47A75, secondary: 15A18; 15A69 | |
| dc.title | On the Higher-Order Derivatives of Spectral Functions: Two Special Cases | |
| dc.type | text |