Local Sensitivity Analysis and Matrix Derivatives
This paper discusses two types of matrix by matrix derivatives; the B-type derivative, introduced by Balestra (1976) and the new defined A-type derivative, because of the arrangement in a “anti-Kronecker” type fashion. Both types of derivatives are linked by permutation matrices (also called commutation matrices by Magnus & Neudecker (1979)), a special type of 0/1-matrices. Section 2.1 gives a- short introduction to matrix derivatives, while the algebra of derivatives implied by these concepts can be found in Balestra (1976) and in Polasek (1980). A-and B-type derivatives allow different partitions of derivative matrices and therefore different ways of interpretations.
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