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Basically derivatives and integrals of matrices parallel derivatives and
integrals of ordinary functions. The easiest way to figure out
what the derivative or integral will be is to expand the matrix and
then take an element by element derivative or integral.
If we let x be an
vector and let
, where y is an
vector (for example, if
, where A is an
matrix,
then y will be an
vector), then

(3.12.1) 
We will also include the following to our definition:

(3.12.2) 
and

(3.12.3) 
Now we'll list two very useful results.^{3.8} If x is an
vector and A is an
matrix of elements
that are not functions of x, then

(3.12.4) 
If A is an
matrix of elements that are not
functions of x, then

(3.12.5) 
and if A is symmetric, that is
, then
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Frank Starmer
20040519