Lewis Carroll Computed Determinants

4 months ago

Charles Dodgson, known as Lewis Carroll, developed a method for calculating determinants called Dodgson condensation.
The method involves repeatedly condensing a matrix by replacing elements with the determinant of 2×2 submatrices formed by neighboring elements.
Dodgson's original 1867 paper is noted for its readability despite changes in mathematical notation over time.
The algorithm includes a division step, requiring precautions to avoid division by zero, such as rearranging rows or columns.
Dodgson's condensation is efficient, with a time complexity of O(n³), and is parallelizable as each 2×2 determinant can be computed simultaneously.
Unlike Gaussian elimination, Dodgson's method maintains integer entries throughout if the original matrix is integer-valued.
The article clarifies a common confusion between cofactor expansion and Cramer’s Rule, emphasizing the former's relevance to determinant calculation.
A question is raised about a potential connection between Dodgson condensation and eigenvalue computation techniques like deflation, though the analogy may be superficial.

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