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The full-rank LDL∗ decomposition of a polynomial Hermitian matrix is examined. Explicit formulae are given evaluating the coefficients of matrices lij and djj. Also, a new method is developed, based on the LDL∗ factorization of the matrix product A∗A, for symbolic computation of the Moore-Penrose inverse matrix. The paper follows the results of [I.P. Stanimirovi´c, M.B. Tasi´c, Computation of generalized inverses by using the LDL∗ decomposition, Appl. Math. Lett., 25 (2012), 526–531], where the matrix products A∗A, AA∗ and the corresponding LDL∗ factorizations are considered in order to compute the generalized inverse of A.
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