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.
All Science Journal Classification (ASJC) codes
- Change-of-variables in integration
- Fourier transform
- Generalized pythagorean theorem
- Matrix volume
- Radon transform
- Surface integrals