The Change-of-Variables Formula Using Matrix Volume
Adi Ben-Israel · SIAM Journal on Matrix Analysis and Applications · 1999
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.