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Two transformation matrices are introduced, L and D, which contain zero and unit elements only. If A is an arbitrary (n, n) matrix, L eliminates from vecA the supradiagonal elements of A, while D performs the inverse transformation for symmetricA. Many properties of L and D are derived, in particular in relation to Kronecker products. The usefulness of the two matrices is demonstrated in three areas of mathematical statistics and matrix algebra: maximum likelihood estimation of the multivariate normal distribution, the evaluation of Jacobians of transformations with symmetric or lower triangular matrix arguments, and the solution of matrix equations.
Magnus et al. (Mon,) studied this question.
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