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In 1866, Charles Ludwidge Dodgson published a paper concerning a method forevaluating determinants called the condensation method. His paper documented anew method to calculate determinants that was based on Jacobi's Theorem. Thecondensation method is presented and proven here, and is demonstrated by aseries of examples. The condensation method can be applied to a number ofsituations, including calculating eigenvalues, solving a system of linearequations, and even determining the different energy levels of a molecularsystem. The method is much more efficient than cofactor expansions,particularly for large matrices; for a 5 x 5 matrix, the condensation methodrequires about half as many calculations. Zeros appearing in the interior of amatrix 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 finddeterminants. This paper presents an elementary proof of Dodgson's method.

An Elementary Proof of Dodgson's Condensation Method for Calculating Determinants