Laplace's rule may be used to compute a version of this quantity for its namesake tensor in order to prove the Alon-Tarsi conjecture for Latin squares of even order; that proof uses Cayley's version of this operator. The Cauchy- Binet rule generalizes it to commutative rings, while Leibniz's formula uses permutations of elements to compute it. Setting to zero the result of
Laplace's rule may be used to compute a version of this quantity for its namesake tensor in order to prove the Alon-Tarsi conjecture for Latin squares of even order; that proof uses Cayley's version of this operator. The Cauchy- Binet rule generalizes it to commutative rings, while Leibniz's formula uses permutations of elements to compute it. Setting to zero the result of this operation on lambda I minus A allows us to calculate A's eigenvalues. Cramer's rule uses ratios of these to solve systems of linear equations. For ten points, name this quantity that is a d minus c b for a 2 by 2 matrix a b c d.
Laplace's rule may be used to compute a version of this quantity for its namesake tensor in order to prove the Alon-Tarsi conjecture for Latin squares of even order; that proof uses Cayley's version of this operator.
{det}erminant