The General Method
This algorithm can be described in the following 4 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 . 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.
- 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.
- 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:
“Towards him they bend
With awful reverence prone; and as a God
Extoll him equal to the highest in Heav’n:
Nor fail’d they to express how much they prais’d,
That for the general safety he despis’d
His own: for neither do the Spirits damn’d
Loose all thir vertue; lest bad men should boast
Thir specious deeds on earth, which glory excites,
Or close ambition varnisht o’er with zeal.”
—John Milton (1608–1674)
“... [a] girl one day flared out and told the principal “the only mission opening before a girl in his school was to marry one of those candidates [for the ministry].” He said he didn’t know but it was. And when at last that same girl announced her desire and intention to go to college it was received with about the same incredulity and dismay as if a brass button on one of those candidate’s coats had propounded a new method for squaring the circle or trisecting the arc.”
—Anna Julia Cooper (1859–1964)