  In 1866, Charles Ludwidge Dodgson published a paper concerning a method for
evaluating determinants called the condensation method. His paper documented a
new method to calculate determinants that was based on Jacobi's Theorem. The
condensation method is presented and proven here, and is demonstrated by a
series of examples. The condensation method can be applied to a number of
situations, including calculating eigenvalues, solving a system of linear
equations, and even determining the different energy levels of a molecular
system. The method is much more efficient than cofactor expansions,
particularly for large matrices; for a 5 x 5 matrix, the condensation method
requires about half as many calculations. Zeros appearing in the interior of a
matrix can cause problems, but a way around the issue can usually be found.
Overall, Dodgson's condensation method is an interesting and simple way to find
determinants. This paper presents an elementary proof of Dodgson's method.
