The link to my article, in The College Mathematics Journal, Vol. 38, No. 2 (Mar., 2007), pp. 85-95, can be found here:

http://www.jstor.org/stable/pdfplus/27646442.pdf?acceptTC=true

The article is titled: “Shutting up like a telescope”: Lewis Carroll’s “Curious” Condensation Method for Evaluating Determinants.

The article introduces the condensation method for finding the determinant of nxn matrices with n>3.

Instead of the rather tedious method of cofactor expansion, the condensation method is used.

The steps are as follows:

Remove all zeros from the interior of A, using elementary row and column operations. Call the matrix A^((0))

Find the determinant of every 2 x 2 consecutive minor in A^((0)) to form a new (n-1) x (n-1) matrix A^((1)) Now find the determinant of every 2 x 2 consecutive minor in A^((1)) to produce an (n-2) x (n-2) matrix. Then divide each term by the corresponding entry in the interior of matrix A^((0)). This will give a new matrix A^((2)).

In general, given the matrix A^((k)), compute a new (n-k-1) x (n-k-1) matrix made up of the determinants of the 2 x 2 consecutive minors of A^((k)).To produce A^((k+1)), divide eacho of these entries by the corresponding entry in the interior of A^((k-1)).

Continue repeating the previous step, condensing the matrix until a single number is obtained. This will be det(A).

This method was invented by Reverend Charles Lutwidge Dodgson (1832-1898), a Church of England clergyman who earned his living as a mathematics lecturer at Christ Church, Oxford. However, under the pseudonym Lewis Carroll, he wrote *Alice in Wonderland*.

It is always interesting when great creativity is found in a mathematician. This method of finding determinants of matrices larger that 2×2 has already come in handy at the tutoring center when helping out linear algebra students. While it is tricky, it does make the process quite a bit easier. Thanks Shannon 🙂

I was not aware of the condensation method for evaluating determinants. While it is a bit complicated, the creativity behind it is astounding.