Title of article :
A Note About Measures, Jacobians and Moore–Penrose Inverse
Author/Authors :
Díaz-García ، José Antonio Facultad de Zootecnia y Ecología - Universidad Autónoma de Chihuahua , Caro-Lopera ، Francisco José Faculty of Basic Sciences - Universidad de Medellín
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.
Keywords :
Jacobian , Matrix differentiation , Hausdorff measure , Lebesgue measure , Generalised inverse
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
