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
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