This operation gives the volume of a parallelopiped of arbitrary dimension.
The Berizinian generalizes this operation to superalgebras. Applying this operation to the metric tensor and taking the square root gives the volume form on a manifold. This operation gives the volume of a parallelopiped of arbitrary dimension. Applying it to successive derivatives of functions is used to conclude whether the functions are linearly independent. In addition to the Wronskian type of this operation, applying it to the Jacobian gives the change of basis formula. A matrix is invertible if and only if this operation is nonzero. A ratio of two of these is used to solve linear systems via Cramer's rule. For 10 points, name this operation that for a 2 by 2 matrix with elements a, b, c, and d is given by ad minus bc.
The Berizinian generalizes this operation to superalgebras. Applying this operation to the metric tensor and taking the square root gives the volume form on a manifold.
determinant [accept det]