4 Vector/Matrix Derivatives and Integrals

4 Vector/Matrix Derivatives and IntegralsThe operations of differentiation and integration of vectors and matrices arelogical extensions of the corresponding operations on scalars. There are threeobjects involved in this operation: the variable of the operation; the operand (the function being differentiated or integrated); and the result of the the simplest case, all three of these objects are of the same type, andthey are scalars. If either the variable or the operand is a vector or a matrix,however, the structure of the result may be more complicated. This statementwill become clearer as we proceed to consider specific this chapter, we state or show the form that the derivativetakes interms of simpler Derivatives . We state high-level rules forthe nature of thedifferentiation in terms of simple partial differentiation of a scalar with respectto a scalar.

Vector/Matrix Derivatives and Integrals ... purpose of this chapter is not to develop a calculus for vectors and matrices ... Matrix Algebra c 2007 James E. Gentle. 146 4 Vector/Matrix Derivatives and Integrals to the variable with which the differentiation is taken. If both the function

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  Vector, Calculus, Algebra

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