Ratios of these functions can be used solve linear equations by Cramer's Rule.
Helmholtz separability depends on one of these due to St?kel. These mathematical objects have a property known as n-linearity. There is a Sylvester identity and Cauchy theorem about them. A version of them is applicable to quadratic forms. The cross product can be generalized to n dimensions if it is treated as one of these operations performed on n minus one n-vectors, a fact often exploited in 3-space. Ratios of these functions can be used solve linear equations by Cramer's Rule. If this vanishes for a matrix, the matrix is called singular. FTP, what is this matrix function that, for a 2-by-2 matrix a b c d, is ad minus bc?
Helmholtz separability depends on one of these due to St?kel.
determinant