This quantity can be defined directly through transformations of the totally antisymmetric permutation tensor, and the problem of finding the largest one for some set of values was posed by Hadamard.
This quantity can be defined directly through transformations of the totally antisymmetric permutation tensor, and the problem of finding the largest one for some set of values was posed by Hadamard. The Cayley-Menger form gives the volume of a simplex in n dimensions, while the "hyper" form of this quantity is defined for tensors of rank higher than two. Solving the eigenvalue problem requires setting this quantity to zero, and a system of linear equations will have a unique solution if this quantity of the associated with the system's matrix is nonzero, according to Cramer's Rule. Typically computed by expansion in cofactors, for ten points, identify this function defined for square matrices, which for a two by two matrix with entries a, b, c, d, is given by ad minus cb.
This quantity can be defined directly through transformations of the totally antisymmetric permutation tensor, and the problem of finding the largest one for some set of values was posed by Hadamard.
{determinant}