On the relationship between the matrix operators, vech and vecd

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1 Citation (Scopus)


We introduce a matrix operator, which we call “vecd” operator. This operator stacks up “diagonals” of a symmetric matrix. This operator is more convenient for some statistical analyses than the commonly used “vech” operator. We show an explicit relationship between the vecd and vech operators. Using this relationship, various properties of the vecd operator are derived. As applications of the vecd operator, we derive concise and explicit expressions of the Wald and score tests for equal variances of a multivariate normal distribution and for the diagonality of variance coefficient matrices in a multivariate generalized autoregressive conditional heteroscedastic (GARCH) model, respectively.

Original languageEnglish
Pages (from-to)3252-3268
Number of pages17
JournalCommunications in Statistics - Theory and Methods
Issue number13
Publication statusPublished - 2018 Jul 3


  • Orthogonal matrix
  • Permutation matrix
  • Symmetric matrix
  • Wald test
  • vecd
  • vech

ASJC Scopus subject areas

  • Statistics and Probability


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