A Note About Measures, Jacobians and Moore–Penrose Inverse

José Antonio Díaz-García, Francisco José Caro-Lopera

Research output: Contribution to journalArticlepeer-review


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
Pages (from-to)55-62
Number of pages8
JournalBulletin of the Iranian Mathematical Society
Issue number1
StateAccepted/In press - 1 Jan 2020


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


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