If this object is zero, its associated array is singular.
Uniquely, this associative multilinear operation commutes with similarity transforms and with both parts of Hermitian conjugation. A set of homogeneous, linear alegbraic equations can have a non-trivial solution only if the one of these corresponding to the coefficients is zero. Ratios of these give the solutions to inhomogeneous linear alegbraic equations through Cramer's rule. If this object is zero, its associated array is singular. This operation maps the square matrices over a set of numbers onto that set, returning an alternating sum of products of the matrix entries. For 10 points, name this operation given for a square matrix a, b, c, d as ad minus bc.
Uniquely, this associative multilinear operation commutes with similarity transforms and with both parts of Hermitian conjugation.
the {determinant}