1980/12/01 by Jan R. Magnus, Heinz Neudecker · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Statistical and numerical algorithms #Scientific Research and Discoveries #Mathematics #Matrix (chemical analysis) #Kronecker product #Transformation (genetics) #Kronecker delta #Triangular matrix #Algebra over a field #Applied mathematics #Inverse #Single-entry matrix #Pure mathematics #Combinatorics #Symmetric matrix #Matrix function #Invertible matrix #Eigenvalues and eigenvectors #Geometry
paper · doi:10.1137/0601049
openalex publication_date 1980/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.