I have 3 n-dimensional vectors and I wanted to compute the 3d volume enclosed by them. I had the following process in mind.
- Perform Gram-Schmidt orthonormalization of the 3 vectors to obtain an orthonormal basis.
- Compute the coefficients of the 3 vectors wrt the orthonormal basis.
- Compute the determinant of the resultant coefficient matrix.
Is there a simpler approach to do this that doesn't involve basis computation?