A function Fn: (M(n,K))→K is defined in terms of the determinant function on M(n.K). It is shown that Fn is n-multilinear. Also, it is observed that a function defined analogously in terms of the permanent function on M(n,K) is n-multilinear. Fn is then expressed in terms ...
If the set has the same number of vectors as each vector has components, which frequently is the case, then there is a calculation to test for linear dependence. Array the vectors in a square matrix and calculate its determinant. If the determinant is 0, they are dependent, and otherwise ...