Abstract
We derive a lower bound on determinants, utilizing a theorem of linear programming. Let l and u be positive lower and upper bounds on the moduli of the eigenvalues of a real or complex invertible matrix A. If the modulus of the trace of A is at least nl, n the dimension of A, we derive a better lower bound on the determinant of A than the trivial lower bound, ln . In particular, given a diagonally dominant real matrix with positive diagonal entries, our lower bound is applicable and improves the lower bound derivable from Gerschgorin's circle theorem. We describe the application of the lower bound as an auxiliary result in representing square roots, the number , and e x , as the limiting quotient of Toeplitz determinants.