— 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.
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.
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