Full-rank block LDL decomposition and the inverses of n× n block matrices.

Full-rank block LDL decomposition of a Hermitian n× n 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 n× n block matrix. The method for the calculation of the Moore-Penrose inverse of an arbitrary 2×2 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. [ABSTRACT FROM AUTHOR]