Matrix Differential Calculus with Applications in Statistics and Econometrics

Magnus & Neudecker — matrix differential calculus

Result

Part Three, Chapter 8 "Some important differentials": §8.3 "The differential of a determinant" (p. 149, $d|X|=|X|\operatorname{tr}X^{-1}dX$), §8.4 "The differential of an inverse" (p. 151); Chapter 9 §9.10 "Scalar functions of a matrix, II: determinant" (p. 178).

Use

the two differentials behind O7's influence function.

Verification

contents scan (primary record, GBV catalogue PDF held in papers/local/); the scan's edition is not identified on the page, and the 2019 edition renumbers — verify page numbers before citing them (5 Sep 2026).