A Note About Measures, Jacobians and Moore–Penrose Inverse

José Antonio Díaz-García; Francisco José Caro-Lopera

doi:10.1007/s41980-020-00365-x

A Note About Measures, Jacobians and Moore–Penrose Inverse

José Antonio Díaz-García, Francisco José Caro-Lopera

Grupo de Investigación en Materiales Nanoestructurados y Biomodelación

Research output: Contribution to journal › Article › peer-review

Abstract

Some general problems of Jacobian computations in non-full rank matrices are revised in this work. We prove that the Jacobian of the Moore–Penrose inverse derived via matrix differential calculus is incorrect. In addition, the Jacobian in the full rank case is derived under the simple and old theory of the exterior product.

Original language	English
Journal	Bulletin of the Iranian Mathematical Society
DOIs	https://doi.org/10.1007/s41980-020-00365-x
State	Accepted/In press - 1 Jan 2020

Keywords

Generalised inverse
Hausdorff measure
Jacobian
Lebesgue measure
Matrix differentiation

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10.1007/s41980-020-00365-x

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