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 (Eves 1996, p. 130). 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_(ij)] with a_(ii)!=0 by forming the (n-1)×(n-1) matrix B=[b_(ij)] such that
b_(ij)=a_(1,1)a_(i+1,j+1)-a_(1,j+1)a_(i+1,1).