A method of revise matrix of small rank for removing influence of additional mass, damping, and stiffness from dynamic response of structures is established.

We call the matrix A as(m,l)rank-idempotent matrix if there exist natural numbers m,l(m>l)such that r(A~m)=r(A~l);when A~m=A~l,then A is called(m,l)idempotent matrix.

The Bott-Duffin inverse and generalized Bott-Duffin inverse of rank-one modified matrix;

In this paper the generalized singular value decomposition of a matrix is used to study the oblique generalized inverse of modified matrix A-CB, where CB is a full rank factorization.

Considering the shortcoming of the matrix updating methods which can not preserve the physical connectivity and has a low computational efficiently,a new updating method with an SVD(singular value decomposition) model is presented based on the theories of multi degrees of freedom vibration and SVD.