Content deleted Content added
Tweak cites, harvnb |
m Substing templates: {{Format ISBN}}. See User:AnomieBOT/docs/TemplateSubster for info. |
||
Line 109:
== Hessian ==
Symmetric <math>n \times n</math> matrices of real functions appear as the [[Hessian matrix|Hessians]] of twice differentiable functions of <math>n</math> real variables (the continuity of the second derivative is not needed, despite common belief to the opposite<ref>{{Cite book |last=Dieudonné |first=Jean A. |title=Foundations of Modern Analysis |publisher=Academic Press |year=1969 |chapter=Theorem (8.12.2) |page=180 |isbn=
Every [[quadratic form]] <math>q</math> on <math>\mathbb{R}^n</math> can be uniquely written in the form <math>q(\mathbf{x}) = \mathbf{x}^\textsf{T} A \mathbf{x}</math> with a symmetric <math>n \times n</math> matrix <math>A</math>. Because of the above spectral theorem, one can then say that every quadratic form, up to the choice of an orthonormal basis of <math>\R^n</math>, "looks like"
| |||