The change-of-variables formula using matrix volume

Adi Ben-Israel

doi:10.1137/S0895479895296896

The change-of-variables formula using matrix volume

Adi Ben-Israel

Mgmt Science & Info Systems

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

16 Scopus citations

Abstract

The matrix volume is a generalization, to rectangular matrices, of the absolute value of the determinant. In particular, the matrix volume can be used in change-of-variables formulae, instead of the determinant (if the Jacobi matrix of the underlying transformation is rectangular). This result is applicable to integration on surfaces, illustrated here by several examples.

Original language	English (US)
Pages (from-to)	300-312
Number of pages	13
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	21
Issue number	1
DOIs	https://doi.org/10.1137/S0895479895296896
State	Published - Jan 1 1999

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Change-of-variables in integration
Determinants
Fourier transform
Generalized pythagorean theorem
Jacobians
Matrix volume
Radon transform
Surface integrals

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