The change-of-variables formula using matrix volume

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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 languageEnglish (US)
Pages (from-to)300-312
Number of pages13
JournalSIAM Journal on Matrix Analysis and Applications
Volume21
Issue number1
DOIs
StatePublished - 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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