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