奇异矩阵求逆的处理方法

The spectral decomposition of a square matrix is X=PAP’, where P is a matrix containing the eigenvector and A is a diagonal matrix with the eigenvalues as the diagonal elements. So the inverse of X is given by PA^(-1)P’. So simply replace the diagonal elements of A by its inverse, one can get the inverse. But when X is a singular matrix, some of the eigenvalues will be close to zero and the inverse will be close to infinity. So one way to get its inverse is to replace those large values (the inverse of very small eigenvalues) by zero, then do PA^(-1)P’.