Formulation
Let A be an n × n matrix with entries in a commutative ring, and Aij (i, j = 1, 2) denote its (n − 1) × (n − 1) submatrices of A formed by the (n − 1) first (i = 1) or last (i = 2) rows, and the (n − 1) first (j = 1) or last (j = 2) columns. Let B be the (n − 2) × (n − 2) submatrix of A formed by the rows and columns from 2 to n − 1. The Lewis Carroll identity states that
If the matrix B is nonsingular, then dividing by its determinant leads to an expression for the determinant of A in terms of the determinants of orders 1 and 2 lower than the order of A. Recursive application of this procedure is the method of Dodgson condensation.
Read more about this topic: Lewis Carroll Identity
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The formulation was used as a motto by the English Nonconformist clergyman Richard Baxter (1615-1691)
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