Fc Swto 2FM

— n,s n3s — /¡¡s nls c nts /ijj rtjj — /Jji C KyS

This example shows that the matrix elements of f(M) are not the functions f of the matrix elements of M, in general.

C.8 Vector Calculus

Let \$ be a scalar function of the n arguments XltX^...,X„. We consider-the arguments to be the components of a column vector

The n partial derivatives of <j> with respect to the elements of X are the components of the gradient of <f>, denoted by d<(> _

Note that d<j>/dX is considered a 1 Xn row matrix. If we eliminate the function <j> from Eq. (C-80). we obtain the gradient operator a ax a__a_ _a_

The matrix product of the 1 Xn gradient operator with annxl vector Y yields a scalar, the divergence of Y, which we denote by ay.

Tx-W

The dot is used to emphasize the fact that the divergence is a scalar, although the usage is somewhat different from that in Eq. (C-23).

The mn partial derivatives of an m-dimensiona! vector Y with respect to Xx,X2 Xn can be arranged in an mx n matrix denoted by ay.