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

Nanostructured Materials and Biomodeling Research Group

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
Pages (from-to)	55-62
Number of pages	8
Journal	Bulletin of the Iranian Mathematical Society
Volume	47
Issue number	1
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

Cite this

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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.",

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author = "D{\'i}az-Garc{\'i}a, {Jos{\'e} Antonio} and Caro-Lopera, {Francisco Jos{\'e}}",

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KW - Hausdorff measure

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KW - Lebesgue measure

KW - Matrix differentiation

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A Note About Measures, Jacobians and Moore–Penrose Inverse

Abstract

Keywords

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