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In mathematics, Dodgson condensation is a method of computing the determinants of square matrices. It is named for its inventor, Charles Dodgson (better known as Lewis Carroll). The method in the case of an ''n'' × ''n'' matrix is to construct an (''n'' − 1) × (''n'' − 1) matrix, an (''n'' − 2) × (''n'' − 2), and so on, finishing with a 1 × 1 matrix, which has one entry, the determinant of the original matrix. ==General method== This algorithm can be described in the following four steps: # Let A be the given ''n'' × ''n'' matrix. Arrange A so that no zeros occur in its interior. An explicit definition of interior would be all ai,j with . One can do this using any operation that one could normally perform without changing the value of the determinant, such as adding a multiple of one row to another. # Create an (''n'' − 1) × (''n'' − 1) matrix B, consisting of the determinants of every 2 × 2 submatrix of A. Explicitly, we write # Using this (''n'' − 1) × (''n'' − 1) matrix, perform step 2 to obtain an (''n'' − 2) × (''n'' − 2) matrix C. Divide each term in C by the corresponding term in the interior of A so . # Let A = B, and B = C. Repeat step 3 as necessary until the 1 × 1 matrix is found; its only entry is the determinant. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dodgson condensation」の詳細全文を読む スポンサード リンク
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