A Note About Measures, Jacobians and Moore–Penrose Inverse

José Antonio Díaz-García, Francisco José Caro-Lopera

Research output: Contribution to journalArticlepeer-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 languageEnglish
JournalBulletin of the Iranian Mathematical Society
DOIs
StateAccepted/In press - 1 Jan 2020

Keywords

  • Generalised inverse
  • Hausdorff measure
  • Jacobian
  • Lebesgue measure
  • Matrix differentiation

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