Dodgson Condensation - The General Method

The General Method

This algorithm can be described in the following 4 steps:

  1. 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 . We can do this using any operation that we could normally perform without changing the value of the determinant, such as adding a multiple of one row to another.
  2. Create an (n − 1) × (n − 1) matrix B, consisting of the determinants of every 2 × 2 submatrix of A. Explicitly, we write
  3. 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.
  4. Let A = B, and B = C. Repeat step 3 as necessary until the 1 × 1 matrix is found; its only entry is the determinant.

Read more about this topic:  Dodgson Condensation

Famous quotes containing the words general and/or method:

    When General Motors has to go to the bathroom ten times a day, the whole country’s ready to let go. You heard of that market crash in ‘29? I predicted that.... I was nursing a director of General Motors. Kidney ailment, they said; nerves, I said. Then I asked myself, “What’s General Motors got to be nervous about?” “Overproduction,” I says. “Collapse.”
    John Michael Hayes (b. 1919)

    There is assuredly no more effectual method of clearing up one’s own mind on any subject than by talking it over, so to speak, with men of real power and grasp, who have considered it from a totally different point of view.
    Thomas Henry Huxley (1825–95)