IJPAM: Volume 66, No. 3 (2011)

ON THE HESSIAN OF THE EXPONENTIAL FUNCTION
WITH $n$ VARIABLES

Pavel Trojovský$^1$, Eva Hladíková$^2$
$^{1,2}$Department of Mathematics
Faculty of Natural Sciences
University of Hradec Králové
62, Rokitanského, Hradec Králové, 50003, CZECH REPUBLIC
$^1$e-mail: Pavel.Trojovsky@uhk.cz
$^2$e-mail: Eva.Hladikova@uhk.cz


Abstract.We obtain the explicit formula for the Hessian of the exponential function with $n$ real variables. The derivation of this formula is based on the expression of the Hessian as the sum of $2^{n}$ simplier determinants. These determinants are computed by using several general lemmas which are proved in this article.

Received: November 22, 2010

AMS Subject Classification: 05B20, 11C20

Key Words and Phrases: Laplace expansion, determinant, Hessian matrix, exponential function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3