Full-rank block LDL ? decomposition and the inverses of nn block matrices
Full-rank block LDL ? decomposition of a Hermitian nn block matrix A is examined, where the iterative procedure evaluating the sub-matrices appearing in L and D is provided. This factorization is used to evaluate the inverse and Moore-Penrose inverse of a Hermitian nn block matrix. The method for the calculation of the Moore-Penrose inverse of an arbitrary 22 block matrix is also provided. Therefore, matrix products A ? A and AA ? and the corresponding full-rank block LDL ? factorizations are observed. Also, a simple explicit formulae calculating the solution vector components of the normal system of equations is stated, where the LDL ? decomposition of the system matrix is done.
full-rank ldl ? decomposition block matrix solution vector inverse matrix hermitian matrix moore-penrose inverse matrix 15a09 15a23