The change-of-variables formula using matrix volume

被引：22

作者：

Ben-Israel, A

机构：

[1] Rutgers State Univ, Rutgers Ctr Operat Res, Piscataway, NJ 08854 USA

[2] Indian Stat Inst, New Delhi 110016, India

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1999年 / 21卷 / 01期

关键词：

determinants; Jacobians; matrix volume; change-of-variables in integration; surface integrals; Radon transform; Fourier transform; generalized Pythagorean theorem;

D O I：

10.1137/S0895479895296896

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：300 / 312

页数：13

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