Dodgson’s Method of “Condensation”
Dodgson’s method originally appeared as his first and only
research paper, published by the Royal Society of London in
1866. The following year he included it in a textbook entitled
An Elementary Treatise on Determinants, with their
application to simultaneous linear equations and algebraical
geometry. This work (the only book that Dodgson ever
published on algebra) prompted an appealing—but entirely
unfounded—anecdote. The story goes that Queen Victoria
enjoyed Alice in Wonderland so much that she asked to be sent
the author’s next book, and was slightly bemused when she
received An Elementary Treatise on Determinants! Amusing
though this story is, according to Dodgson, “it is utterly false
in every particular: nothing even resembling it has ever
occurred.” Dodgson called his method “Condensation of
Determinants, being a new and brief method for computing
their arithmetical values,” basing it in part on the following
definition:
Given an n × n matrix A, with n ≥ 3, the interior of A, or
int A, is the (n – 2) × (n – 2) matrix that results when the first
row, last row, first column, and last column are deleted.