pivotal condensation

Chió pivotal condensation is a method for evaluating an n×n determinant in terms of (n - 1)×(n - 1) determinants. It also leads to some remarkable determinant identities. Chiío's pivotal condensation is a special case of Sylvester's determinant identity. Chió's condensation is carried out on an n×n matrix A = [a_(i j)] with a_(i i) !=0 by forming the (n - 1)×(n - 1) matrix B = [b_(i j)] such that b_(i j) = a_(1, 1) a_(i + 1, j + 1) - a_(1, j + 1) a_(i + 1, 1). Then det(A) = (det(B))/a_11^(n - 2).

condensation | determinant | determinant expansion by minors | Sylvester's determinant identity